I guess we can assume that the search would be legal because Columbo really wasn’t searching or even “looking”. He was merely posing as someone who was searching. He didn’t open up any drawers, closets, etc. I don’t know how this would work in real life, but it was reasonable for my suspension of disbelief.
That was also the crime scene, which would give him more latitude than going to the Dr's house for example. He wouldn’t need a warrant to take photos in the building of the crime scene.