What is the meaning of "Notzer Chesed la'Alafim"?
Rashi: He safe-keeps the Chesed that a person does - to reward his offspring up to two thousand generations. 1
In Seifer ha'Pardes, Rashi writes that some commentaries list thirteen Attributes from "Hashem" through to "ve'Chata'ah", counting "Notzer Chesed la'Alafim" as two, whereas others include "ve'Nakeh", and count "Notzer Chesed la'Alafim" as one.
What is the difference between Avon, Pesha and Chata'ah?
Rashi: "Avon" refers to sins performed out of pleasure, "Pesha", to rebellious sins (where the perpetrator does not benefit from the sin), and "Chata'ah", 1 to sins performed inadvertantly.
Seforno: "Avon" refers to sins performed out of pleasure, "Pesha", to rebellious sins, and Chata'ah, to cynical sins, that are performed joyously. 2
And what does "ve'Nakeh Lo Yenakeh mean?
Rashi #1: He does not pardon the sin completely, but enacts punishment slowly, bit by bit.
Rashi #2, Targum Onkelos and Targum Yonasan: He forgives those who do Teshuvah, but not those who don't. 1
Ramban: Hashem carries the various levels of sin and cleanses the sins through reincarnation. 2
Why does Hashem "visit the sins of the fathers on the sons"?
Rashi, Targum Onkelos and Targum Yonasan: He does that only when the sons continue to go in the way of their fathers.
Seforno: This really pertains to people who have sinned to such an extent that there is no hope that they will do Teshuvah, 1 at which point Hashem will punish them.
Which generally occurs when the sins are continually transgressed for a number of generations (Seforno).
Why did Hashem specify the third and the fourth generations?
Seforno: He waits for the sins of the third generation to surpass those of their grandfathers 1 before punishing them, but punishes the fourth generation, even if they just continue sinning like their great-grandfathers.
What is the significance of the difference between the extended times of Hashem's reward and punishment?
Rashi: From the fact that Hashem rewards up to two thousand generations 1 and punishes up to only four generations, we see that His measure of goodness is five hundred times more than His measure of punishment.
The question is asked that, seeing as the world will only last until the year six thousand, there will never be two thousand generations? I once heard an answer to this question based on the Midrash that, when Mashi'ach comes, women will give birth every day.