I know this is jut a movie, but I don't believe Columbo would go with all of this in real life. If in fact he didn't know whether these were the stolen paintings he touched and that was just a hunch, then if Columbo would be wrong he would have nothing on Dale and Dale would know that Columbo suspects him and leave the country or something. The only thing that saves this ending is the reaction of Dale and if that was just Columbo's bluff. Just like the reaction of that detective looking for the contact lense in the trunk of the car. In that episode Columbo himself said, that the reaction of the murderer incriminated him and not the evidence. Maybe Columbo just assumed (basing on how Dale reacted when Columbo wanted to see what he had in the bag), that he touched the stolen paitings in Dale's apartment and risked confronting him with his theory. But that was careless in my opinion. They found fingerprints on the paintings, but at that point they could not know that they were in fact Columbo's. The would have to make the lab verify that. It would be ok for me if Columbo would check it in the lab first and then confront Dale. After being 100% sure his theory was right. Just like in the episode with the General what's-his-name. Columbo FIRST had the pistol checked in the lab and THEN confronted the General about it being the murder weapon.

Columbo also suspected Dale because of the high heels going down the back stairs,what burgler/murderer wears high heels to a house break in.That is why he set up the demonstration with the policewoman and the security guard said that was what he heard.He knew he had a helper and that he was setting up an alibi by asking the valet to look in his trunk for his cufflink and making sure for people to know that he was at the gallery at the time of the murder by asking the time.