I think perhaps big screwups get documented in some sort of informal manner, at least, but I have never heard of anyone being made to sign a statement about it. Then again, I imagine stuff like that would be kept pretty quiet and not passed around.
Speaking of mistakes, though, most mistakes happen out of ignorance or inattention (either deliberate or not - a lot of ignorance is far from deliberate!). The biggest mistake I see residents making is not asking for help, either they think the attending will think less of them or they waited until it was too late to tackle a major specimen and everyone went home, or whatever. I also see many senior residents avoiding giving help, which is unfortunate also.
My biggest lesson to incoming residents: ASK QUESTIONS. I can't think of any attending here who wouldn't offer to go over a difficult specimen (or your first of any specimen) if you ask. They may tell you to ask a senior resident if they are too busy, but no one will ever leave you hanging if you ask.