ABC:Jeremiah 31

Verse 30, Punishment for Ancestor's Sins?
Patheos' Bob Seidensticker claims there is a contradiction here and makes the following comments (italicized):

Do people deserve punishment for their ancestors' sins? The Bible demands intergenerational punishment so that children must be punished for their parents’ sins. Exodus 20:5 Thou shalt not bow down thyself to them, nor serve them: for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me; Jeremiah 16:11 Then shalt thou say unto them, Because your fathers have forsaken me, saith the LORD, and have walked after other gods, and have served them, and have worshipped them, and have forsaken me, and have not kept my law;  But the opposite claim is recorded in the Bible as well. Deuteronomy 24:16 The fathers shall not be put to death for the children, neither shall the children be put to death for the fathers: every man shall be put to death for his own sin. Jeremiah 31:30 But every one shall die for his own iniquity: every man that eateth the sour grape, his teeth shall be set on edge. Ezekiel 18:4 Behold, all souls are mine; as the soul of the father, so also the soul of the son is mine: the soul that sinneth, it shall die. Where does this leave Original Sin? This is the idea that we’re born fallen and deserve hell because of Adam’s sin, which infects us all. What foundation remains for Original Sin if it is undercut by the Bible itself?

The same teachings both appear in the book of Deuteronomy.

Deuteronomy 24:16 the fathers shall not be put to death for the children, neither shall the children be put to death for the fathers: every man shall be put to death for his own sin.

Deuteronomy 5:9-10 thou shalt not bow down thyself unto them, nor serve them: for I the LORD thy God am a jealous God, visiting the iniquity of the fathers upon the children unto the third and fourth generation of them that hate me, and shewing mercy unto thousands of them that love me and keep my commandments.

These commandments were both given to Moses at the same time. While God only commands capital punishment for those who sin, not their children, there are genetic consequences not involving death which occur from sin which affect one's descendants. For example, incest can cause birth defects. In some cases, God even curses the descendants of the wicked. (Psalms 109:13) Thus, children are not put to death for what their parents have done (Deuteronomy 24:16; Ezekiel 18:20), but can to a degree still "bear the iniquity" of their parents' actions in the form of negative circumstances. (Deuteronomy 5:9-10; Exodus 20:5)

Nonetheless, God shows mercy to those who do good, judging them based on their own actions. (Ezekiel 18) God can turn away wrath and consequences as He did from Nineveh. In the case of King Josiah for example his individual righteousness resulted in God delaying a punishment that would have otherwise come upon him. (2 Kings 22:19-20)

As for the doctrine of Original Sin, while sin entered the human race because of Adam and Eve's disobedience, we still are accountable to God based on our free will decisions. (Romans 5:12-21; 1 Corinthians 15:21-22) While we have a sin nature that causes temptation to sin, and become even more enslaved to the sins we engage in (Romans 6:16-21), we are still accountable to God for our sins. Although the Bible calls those righteous who seek after God, doing justice and mercy, nonetheless all our good deeds are like filthy rags before God (Isaiah 64:6), and apart from the salvation in Jesus, our good deeds are all outweighed by our bad ones, so that we would be futilely seeking to outweigh the debts for our sin with good works. (Romans 4:4-8) By works will none be justified. (Galatians 2:16) Only by faith in Jesus can we be justified. (Galatians 3:11)

Verse 34
TheThinkingAtheist.com claims the Bible is wrong about the following passage, and makes the following comments:

Exodus 34:6 And the LORD passed by before him, and proclaimed, The LORD, The LORD God, merciful and gracious, longsuffering, and abundant in goodness and truth, 7 Keeping mercy for thousands, forgiving iniquity and transgression and sin, and that will by no means clear the guilty; visiting the iniquity of the fathers upon the children, and upon the children's children, unto the third and to the fourth generation. God remembers sin.

Jeremiah 31:34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more. God does not remember sin.

The answer to this should be obvious. The covenant is conditional, conditioned upon the repentance of those engaged in sin to turn from their wicked ways. God is willing to forgive utterly those who reject their old evil ways, and makes this clear even in the Old Testament.

Ezekiel 18:21 ¶ But if the wicked will turn from all his sins that he hath committed, and keep all my statutes, and do that which is lawful and right, he shall surely live, he shall not die. 22 All his transgressions that he hath committed, they shall not be mentioned unto him: in his righteousness that he hath done he shall live. 23 Have I any pleasure at all that the wicked should die? saith the Lord GOD: and not that he should return from his ways, and live? 24 But when the righteous turneth away from his righteousness, and committeth iniquity, and doeth according to all the abominations that the wicked man doeth, shall he live? All his righteousness that he hath done shall not be mentioned: in his trespass that he hath trespassed, and in his sin that he hath sinned, in them shall he die. 25 Yet ye say, The way of the Lord is not equal. Hear now, O house of Israel; Is not my way equal? are not your ways unequal? 26 When a righteous man turneth away from his righteousness, and committeth iniquity, and dieth in them; for his iniquity that he hath done shall he die. 27 Again, when the wicked man turneth away from his wickedness that he hath committed, and doeth that which is lawful and right, he shall save his soul alive. 28 Because he considereth, and turneth away from all his transgressions that he hath committed, he shall surely live, he shall not die. 29 Yet saith the house of Israel, The way of the Lord is not equal. O house of Israel, are not my ways equal? are not your ways unequal?

Luke 13:1 ¶ There were present at that season some that told him of the Galilaeans, whose blood Pilate had mingled with their sacrifices. 2 And Jesus answering said unto them, Suppose ye that these Galilaeans were sinners above all the Galilaeans, because they suffered such things? 3 I tell you, Nay: but, except ye repent, ye shall all likewise perish. 4 Or those eighteen, upon whom the tower in Siloam fell, and slew them, think ye that they were sinners above all men that dwelt in Jerusalem? 5 I tell you, Nay: but, except ye repent, ye shall all likewise perish.

To put it simply, the critic put words in God's mouth. The Bible never says in Jeremiah that God never remembers sin at all. God said He would not remember sin for those He was making the New Covenant (i.e. "new testament" or "new contract/agreement") with specifically. If the critic had quoted the full context of the passage this would have been more clear:

Jeremiah 31:31 Behold, the days come, saith the LORD, that I will make a new covenant with the house of Israel, and with the house of Judah: 32 Not according to the covenant that I made with their fathers in the day that I took them by the hand to bring them out of the land of Egypt; which my covenant they brake, although I was an husband unto them, saith the LORD: 33 But this shall be the covenant that I will make with the house of Israel; After those days, saith the LORD, I will put my law in their inward parts, and write it in their hearts; and will be their God, and they shall be my people. 34 And they shall teach no more every man his neighbour, and every man his brother, saying, Know the LORD: for they shall all know me, from the least of them unto the greatest of them, saith the LORD: for I will forgive their iniquity, and I will remember their sin no more.

The entire New Testament is written around this concept, that God will not remember sin for those who repent and trust in Jesus Christ.

Romans 4:6 Even as David also describeth the blessedness of the man, unto whom God imputeth righteousness without works, 7 Saying, Blessed are they whose iniquities are forgiven, and whose sins are covered. 8 Blessed is the man to whom the Lord will not impute sin.