Yes, this is a mistake.
Saw the video below as a suggestion after the one you linked for what to watch next. #7 on the list calls out the bullet holes as a production error. They seem to have done their research on the explanations for each point they raise, so had those holes been there "on purpose" I imagine they would have mentioned why. (Spoiler alert: they don't.)
Also, just FYI, that guy is not Jerry Seinfeld. His (her) name was Robert Arquette (credited on IMDB as Alexis Arquette, as she apparently had gender reassignment surgery at some point after this movie was filmed.)