For a computational problem, can the set of instances be finite?
A finite problem can be decided in O(1) time: we can simply compare the input to a finite (bounded) list of known cases, and emit the output consequently.

Indeed, for that we do not need a Turing powerful system: a finite-state automaton suffices.

So, the problem is indeed trivial.

Co-finite (finite complement) problems are similarly trivial.