So McCoy's outfit changes between shots in the same episode? If that is so, then yeah, that would be a mistake. But if his outfit happens to stay the same in the same episode but different from other episodes, maybe not. I guess I'll take a look.
edit: Did anyone notice that one of the earliest episodes had Scotty wearing the same insignia
he wore later on as identified as a mistake by ZapBrannigan
Are we really so sure as to the meaning of these insignias?