Here's a judgement call:
McCoy wore an engineering insignia on his short-sleeve uniform in "Obsession" and Scotty had a sciences insignia on his red shirt in "The Lights of Zetar." Should CBS have corrected them?
These were accidents, not the intention of the producers.
On the other hand, some of us might take a little joy in being able to spot things like this, and consider them part of the show's true fabric (in much the way that an imperfection in Spock's ears would be part of STAR TREK's actual make-up).
And another one:
Should the incredibly beautiful Dr Ann Mulhall be put into a blue uniform with a sciences patch? It would right a technical wrong, but it wouldn't look as good! This is a conundrum. I suspect (help me out here) that her make-up and lighting may have been done with the red uniform in mind. So, take her out of that dress and what have you got?