It must have been a syndicated British or Australian show---maybe it was American. 2 good natured scalawags, or half-assed detectives------it would always end with the more sophisticated of the two saying something in latin----the other guy would say "which means" and then the answer in English was the punch line.
Later on, Yes, Minister had scenes like you mentioned but I was only an occasional watcher. I also seem to remember Blackadder throwing around a bit of Latin once but certainly not to end each episode. The majority of any shows from the BBC going that far back will likely have been lost forever due to (cringe) wiping tapes for reuse. Still the description may jog a memory.