Were those insignia "mistakes" in TOS really mistakes? I mean, were they ever identified as to mean a specific department in the series or is this something we've retroactively applied to them?
If McCoy always wears the little globe-y one and in one shot has the Fibonacci-spiral one, yup, that's a mistake. Same for Scotty with my (er, I mean his) beloved Mira.
But what a great picture of DeForest Kelley!
And Ann Mulhall could have a doctorate in an engineering field, right? Or does the script contradict that? I think someone on the bbs postulated that as an explanation for her in her fetching red outfit, nom nom.
To answer the question, yes, if you're (CBS) going to add all sorts of cartoon-Enterprise shots and planet scenes, change a couple of patches somehow. My opinion. I don't care about cost, since it's not my money and they've made gazillions off us through Trek.