Discounting character arcs and events which were series-specific, I never got the impression that the Trek
writers were all that concerned about the continuity other than in vague terms. Anything they referenced it, it was more of a fan-wink than anything else (DS9 did this a lot).
The only exception that I can think of is Enterprise
's 4th season where they intentionally played with Trek
continuity, but that was more to do with the fact that TPTB knew the writing was on the wall and went "Fuck it. Lets have some fun".
Not that I'm complaining about Trek
'09's "remake, but not really" approach. It is a perfectly fine way to revitalize a franchise.