If the UV LED is shortwave (under 400nm), you can find stray pee around the toliet, cat pee around the litterbox, dog pee around the bases of walls and doors, and other "messes" or "mistakes" that pets might leave behind around the house.
You can also take an LED like this and shine it at clothes at the thrift store. You can sometimes find "the hidden enemy" under the arms of shirts; assuming the fabric itself doesn't fluoresce and glow too. "The hidden enemy" should glow a bluish white color under the light of a sub-400nm LED - that's the shirt you *don't* want to buy.