For any mistake, I typically will note it if it was noticable by anyone but me (this includes my own mistakes). If the board op was 2 secs late hitting the go, and he knows that it was late, I feel like it is something that can be handled with a brief conversation after the show and doesn't need to be broadcast. I also take responsibility (to management) for small crew errors if I know that it was a one time mental goof up, etc that has already been resolved.
However, if there is a error that is chronic or caused by negligence, then I would definitely note it.