Must a prayer intended as a make-up for yesterday's Dhuhr be repeated if it is later discovered that it had, in fact, already been prayed?

If you intended the Dhuhr prayer of yesterday, this means you did not pray today's Dhuhr, and you must perform it. Your prayer, which you intended for yesterday's Dhuhr, is considered a supererogatory (nafl) prayer. For deeds are by intentions, and if it becomes clear that you made a mistake in the intention of the time, the majority of scholars hold that it does not suffice for the prayer of the present time.