Most people fall in to a few categories:
1. Average people that just watch and enjoy with a very small to non existent regard to continuity.
2. Average trekkie, they have a small to medium regard for continuity, maybe speak up for blatant violations, but in all, just enjoy the show for what it is, and how its presented.
3. Your Anal Trekkie that counts rivits, and posts online of any violaiton of "Sacred Cannon"
so on average, I'd guess that 90% fall into the first 2 categories, they either don't really care, or care enough if something they care about seems screwed up. The unfortuate thing is, cat 3 is the most vocal ( as in almost any topic.. the rivit counters, offended is the most vocal, where most are like, meh..)
Me personaly, am in cat 2, just a reasonable trekkie that has 1 or 2 bugaboos about some things ( enterprise size is one, based off of me building model kits of them, and wanting to display them in some sort of continuity) But on average, I accept what the show is telling me, idiom of " going in with my eyes open, no pre concieved notions, and enjoy the darn show" I might nit pick things afterward, maybe do some sugestions, but in all I enjoy whatever they give me