I wouldn't. I never progressed beyond chess clubs in public schools and I certainly remember people making illegal moves in tournaments. Like that's why they make you both record all the moves. Because people make mistakes. Though, honestly, I remember more notation errors than play errors.

Accidentally moving into check is probably the most common illegal move. Castling though check is surprisingly common, too. Actually moving a piece incorrectly is fairly rare, though. I remember one tournament where one of the matches ended in a DQ because one of the players had two white bishops.