I define continuity as the stories taking place in the same ficticious universe, and ideally all the dots would join up perfectly at the end. BUT, Trek wasn't planned out from the beginning as some epic saga. It's been made up as they went along by generations of writers and producers, and they all had their own slightly different ideas about how the Trek universe should work, should look, and should feel. As a result, minor mistakes have crept in, and some subtle rewrites have taken place.
Viewers are supposed to/expected to suspend their disbelief when watching. We make-believe the guy in the blue makeup and antennae is an alien (who happens to look and sound suspiciously like a couple of other aliens on the other Trek shows
), and we kind of ignore (or possibly forget - I wouldn't know a tenth of the nitpicks I do if it weren't for the internet!) that the old Enterprise zoomed from the rim of the galaxy to Earth and the centre without any trouble when Voyager is taking a lifetime to make a similar journey.
Everyone's mileage varies on how much change they're willing to accept, I guess.
Remember also that Babylon 5, which WAS planned out from the beginning and ran a measly five years compared to Trek's 45 and with the same guy running things the whole time, has some continuity errors too. Nobody's perfect