How Jews stopped stoning people for adultery, or how to improve your holy books

This is from a conversation in another place, but I figured I wanna repost it here.

Torah says that adulterers should be stoned (to be exact, only women's adultery was punishable but they stoned both the married woman and the man who had sex with her).

At some point some of the writers of Talmud figured it might not be such a bright idea after all. They couldn't say that Torah was wrong, of course, but they decided that stoning is such a serious punishment that you need really serious standards of proof: two witnesses. And since they were probably experienced men, they figured that the world is full of morons who'd get caught anyway, so they demanded an additional condition: the culprits have to have been warned in advance not to do it, also by two witnesses.

After that Jews totally stopped committing adultery in front of two disapproving witnesses, and the stoning fell into disuse.