TUC basically hangs its plot on references to 24th century Trek. In a lot of ways STVI is the most displaced TOS movie, because it's the only one where the goal-posts had moved and nearly everybody involved in it's production kind of acknowledged that TOS wasn't the only game in town anymore.
We've talked about how TOS' style and mood clashed quite a bit with TNG's super-nice future, and TUC plays on this clash, as the main crew of TOS deals with a future that's not like what they're used to. A fine last chapter for the original cast.