ABC:Matthew 5

Verse 1
Infidels.org's Meritt claims a contradiction exists here.

Matthew 5:1: And seeing the multitudes, he went up into a mountain: and when he was set, his disciples came unto him: 2 And he opened his mouth, and taught them, saying,

Luke 6:17 And he came down with them, and stood in the plain, and the company of his disciples, and a great multitude of people out of all Judaea and Jerusalem, and from the sea coast of Tyre and Sidon, which came to hear him, and to be healed of their diseases; 18 And they that were vexed with unclean spirits: and they were healed. 19 And the whole multitude sought to touch him: for there went virtue out of him, and healed them all. 20 ¶ And he lifted up his eyes on his disciples, and said, Blessed be ye poor: for yours is the kingdom of God.

Luke 6:17 appears to be separate from 6:20, in other words, Jesus was on a plain healing the sick, the multitude thronged Him, and then He went up into a mountain to teach. This entire sequence is related in order in Mark 3:7-14, including the exact location of Tyre and Sidon's sea coast:

Mark 3:7 But Jesus withdrew himself with his disciples to the sea: and a great multitude from Galilee followed him, and from Judaea, 8 And from Jerusalem, and from Idumaea, and from beyond Jordan; and they about Tyre and Sidon, a great multitude, when they had heard what great things he did, came unto him. 9 And he spake to his disciples, that a small ship should wait on him because of the multitude, lest they should throng him. 10 For he had healed many; insomuch that they pressed upon him for to touch him, as many as had plagues. 11 And unclean spirits, when they saw him, fell down before him, and cried, saying, Thou art the Son of God. 12 And he straitly charged them that they should not make him known. 13 ¶ And he goeth up into a mountain, and calleth unto him whom he would: and they came unto him.

...

Mark 4:1 And he began again to teach by the sea side: and there was gathered unto him a great multitude, so that he entered into a ship, and sat in the sea; and the whole multitude was by the sea on the land. 2 And he taught them many things by parables, and said unto them in his doctrine, 3 Hearken; Behold, there went out a sower to sow:

The Sermon on the Mount appears to have occurred here in the Gospel of Mark, which relates the entire story. First Jesus withdrew with His disciples to the sea coast of Tyre and Sidon and was followed by a great multitude from Galilee, Judea, Jerusalem, Idumaea, Jordan, Tyre, and Sidon. (Luke 6:17, Mark 3:7-8) Jesus went into a ship with His disciples so He wouldn't get crowded by the multitude. (Mark 3:9-12) Jesus then went up to a mountain and taught. (Matthew 5:12, Mark 3:13-35) After all of this Jesus "began again to teach by the sea side" and again entered into a ship, teaching the multitude through parables from the ship. (Mark 4:1-34)

At any rate, both are true, Jesus was at a plain near the sea coast and then went up into a mountain. Mark appears to be the most detailed account of what happened with regards to location and detail. Luke 6:20 then skips all of the information about him moving from the plain to the sea to the mountain back to the sea and just starts the new paragraph talking about his famous sermon. Luke then probably focuses on what the writer considers most relevant, the huge multitude, the miracles, and the sermon, largely bypassing the specific details of the location changes that Mark delves into in detail.

Additionally, see John 6:1-3 for more confirmation that this sequence occurred:

John 6:1 After these things Jesus went over the sea of Galilee, which is the sea of Tiberias. 2 And a great multitude followed him, because they saw his miracles which he did on them that were diseased. 3 And Jesus went up into a mountain, and there he sat with his disciples.

Again, same sequence as before. Jesus crosses over the sea. He is followed by a huge multitude because of His miracles. Jesus then goes up into a mountain with His disciples. There is a transition back and forth from the plain to the sea to the mountain and back to the sea again, but without comparing all accounts this isn't as obvious.

Verse 3
Infidels.org's Meritt claims a contradiction exists here and asks, "How many beatitudes in the Sermon on the Mount" before providing the following list:

Matthew 5:3 Blessed are the poor in spirit: for theirs is the kingdom of heaven. 4 Blessed are they that mourn: for they shall be comforted. 5 Blessed are the meek: for they shall inherit the earth. 6 Blessed are they which do hunger and thirst after righteousness: for they shall be filled. 7 Blessed are the merciful: for they shall obtain mercy. 8 Blessed are the pure in heart: for they shall see God. 9 Blessed are the peacemakers: for they shall be called the children of God. 10 Blessed are they which are persecuted for righteousness' sake: for theirs is the kingdom of heaven. 11 Blessed are ye, when men shall revile you, and persecute you, and shall say all manner of evil against you falsely, for my sake.

Luke 6:20 And he lifted up his eyes on his disciples, and said, Blessed be ye poor: for yours is the kingdom of God. 21 Blessed are ye that hunger now: for ye shall be filled. Blessed are ye that weep now: for ye shall laugh. 22 Blessed are ye, when men shall hate you, and when they shall separate you from their company, and shall reproach you, and cast out your name as evil, for the Son of man's sake. 23 Rejoice ye in that day, and leap for joy: for, behold, your reward is great in heaven: for in the like manner did their fathers unto the prophets.

Obviously it's not a 'contradiction' for one account to give more detail than another since neither passage states "there are X amount of beatitudes." The pattern of the Bible is that some accounts give more detail than others, complementing one another to form a cohesive whole and filling in spots left unexplained elsewhere.

Verse 16: Should Good Works Be Seen? (FFRF)
Dan Barker of FFRF claims there is a contradiction here and makes the following comments (italicized). Jim Meritt of Infidels.org also claims the Bible contradicts itself on good deeds.

Should Good Works Be Seen? Matthew 5:16 Let your light so shine before men, that they may see your good works, and glorify your Father which is in heaven. 1 Peter 2:12 Having your conversation honest among the Gentiles: that, whereas they speak against you as evildoers, they may by your good works, which they shall behold, glorify God in the day of visitation. vs. Matthew 6:1-4 ¶ Take heed that ye do not your alms before men, to be seen of them: otherwise ye have no reward of your Father which is in heaven. Therefore when thou doest thine alms, do not sound a trumpet before thee, as the hypocrites do in the synagogues and in the streets, that they may have glory of men. Verily I say unto you, They have their reward. But when thou doest alms, let not thy left hand know what thy right hand doeth: That thine alms may be in secret: and thy Father which seeth in secret himself shall reward thee openly. Matthew 23:3-5 All therefore whatsoever they bid you observe, that observe and do; but do not ye after their works: for they say, and do not. For they bind heavy burdens and grievous to be borne, and lay them on men's shoulders; but they themselves will not move them with one of their fingers. But all their works they do for to be seen of men: they make broad their phylacteries, and enlarge the borders of their garments,

Jesus when doing miracles took this a step further, strictly telling those He healed not to tell anyone about what He'd done. (Mt. 8:4; 9:30; 12:16; Mk. 5:43; 7:36; Lk. 5:14; 8:56) As should be readily apparent, there is no contradiction here. Matthew 5:16 does not say to do good works before all - obviously those receiving alms will "see your good works and glorify your Father which is in Heaven." Matthew 5:16 is not a commandment to do alms openly in contradiction of 6:3, but to do them at all.

Verse 17 (Changing Rules)
Patheos' Bob Seidensticker claims there is a contradiction here and makes the following comments (italicized):

God's rules keep changing God made an “everlasting covenant” with Abraham, but then he tore that one up and made another one with Moses. The New Testament continues the confusion. It can’t decide whether to look backwards and honor existing law or to tear it up yet again, because it says both. First, Jesus commits to existing law: Matthew 5:17-18 ¶ Think not that I am come to destroy the law, or the prophets: I am not come to destroy, but to fulfil. For verily I say unto you, Till heaven and earth pass, one jot or one tittle shall in no wise pass from the law, till all be fulfilled. But then the book of Hebrews weaves a legal case that argues that Jesus is a priest in the line of Melchizedek, which ought to take priority over the existing priesthood in the line of Aaron. Here it quotes an Old Testament declaration of God to justify a new covenant. Hebrews 8:6-13 ¶ But now hath he obtained a more excellent ministry, by how much also he is the mediator of a better covenant, which was established upon better promises. For if that first covenant had been faultless, then should no place have been sought for the second. For finding fault with them, he saith, Behold, the days come, saith the Lord, when I will make a new covenant with the house of Israel and with the house of Judah: Not according to the covenant that I made with their fathers in the day when I took them by the hand to lead them out of the land of Egypt; because they continued not in my covenant, and I regarded them not, saith the Lord. For this is the covenant that I will make with the house of Israel after those days, saith the Lord; I will put my laws into their mind, and write them in their hearts: and I will be to them a God, and they shall be to me a people: And they shall not teach every man his neighbour, and every man his brother, saying, Know the Lord: for all shall know me, from the least to the greatest. For I will be merciful to their unrighteousness, and their sins and their iniquities will I remember no more. In that he saith, A new covenant, he hath made the first old. Now that which decayeth and waxeth old is ready to vanish away. Jesus is a dramatic change to Judaism, and there must be some logic to justify Christians changing their worship day, dropping the sacrifices, worshiping a new guy in addition to Yahweh, and so on. That rationalizes away one problem, but the overall problem—the various substories don’t fit together in the overall plot—remains. (More: “The Bible Story Reboots. Have You Noticed?”)

First of all, God never nullified His covenant with Abraham when making a covenant with Moses, that is a blatant mischaracterization by the critic. God's covenant with Abraham was that Abraham's descendants would have the land of Israel, while circumcising their male children and worshiping God. (Genesis 17:7-21; 15:17-21) This commandment was continued under Moses. (Leviticus 12:3). It was certainly not inconsistent or discontinued under the Mosaic Law, indeed Jews today continue to practice circumcision.

Secondly, the new covenant under Jesus that the critic refers to in Hebrews 8 was foretold centuries earlier by the prophet Jeremiah; indeed Hebrews 8 is quoting exactly what Jeremiah said. (Jeremiah 31:31-34) Moses himself told the Israelites that God would raise them up a Prophet to bring them new commandments, and that the Israelites would be punished if not listening to that Prophet. (Deuteronomy 18:15-19) The New Testament repeatedly states that Jesus is that Prophet. (John 1:45; Acts 3:22-23; 7:37)

Thirdly, nothing in the New Testament requires that Christians meet on Sunday rather than Saturday. According to John Calvin in 'Instruction in Faith' the change from Saturday to Sunday was made to avoid legalism by Jewish Christians. To quote Calvin, "As our human weakness does not allow such assemblies to meet every day, the day observed by the Jews has been taken away (as a good device for eliminating superstition) and another day has been destined to this use. This was necessary for securing order and peace in the Church." However, such a practice is not based upon any explicit New Testament teaching.

Fourthly, Israel has long since stopped the sacrifices regardless. This occurred, as prophesied in Daniel 9:25-27, following the destruction of the Temple in Jerusalem in A.D. 70 by Nero. God said, long before Jesus arrived, that He disapproved of the Jewish sacrifices and sabbaths, taking no pleasure in them. (Isaiah 1:11-15; 66:3; Hosea 6:6; Jeremiah 7:22-23; Psalms 51:16-19; 40:6; 50:8-15; 1 Samuel 15:22) Daniel's prophecy, by the way, perfectly predicted that the Messiah would arrive 483 years (69 weeks of years) after the rebuilding of Jerusalem (444/445 B.C.; cp. Nehemiah 2:1) so the Messiah should have arrived around 38/39 A.D. For more on this, see Scientific Evidence.

Fifthly, the one the Israelites were worshiping was always Jesus. What many people don't realize is that when God spoke to Moses originally in the burning bush, to Abraham even earlier, and to Jacob, it was not God the Father speaking, but the 'Angel of the Lord' who spoke. (Exodus 3:2-4; Genesis 22:15-18; 31:11-13; 32:28-30; 48:16) Jesus Himself said He was the original God of the Israelites. (John 8:56-58) For that reason it is written that Jesus came to His own and they did not receive Him. (John 1:11; cp. Isaiah 53:3-4) For more on Jesus as the Angel of the Lord, see Christophanies.

Verse 39
American Atheist's list at American Atheists claims this is a contradiction.

Personal Injury

“... thou shalt give life for life, Eye for eye, tooth for tooth, hand for hand, foot for foot. burning for burning, wound for wound, stripe for stripe. ”

Exodus 21:23-25 Exodus 21:23 And if any mischief follow, then thou shalt give life for life, Eye for eye, tooth for tooth, hand for hand, foot for foot, Burning for burning, wound for wound, stripe for stripe.

“... ye resist not evil: but whosoever shall smite thee on the right cheek, turn to him the other also.”

Matthew 5:39 But I say unto you, That ye resist not evil: but whosoever shall smite thee on thy right cheek, turn to him the other also.

The Old Testament commandment of "eye for an eye" did not justify taking vengeance for wrongs done to oneself. The Israelites even then were commanded not to harm others out of vengeance (Lev. 19:18; Prov. 20:22). The commandment of "eye for an eye" allowed governmental execution of justice for the sake of order in society; not out of vengeance but to promote good in the world and stop those who harm others from overrunning society given a lack of consequences. That same principle is repeated in the New Testament, that governments "bear the sword" under God's authority to punish those who do evil. (Rom. 13:4)