Plot hole: Columbo is in the Pauley's hotel room trying to figure out how the bottle landed upright next to his body after he was shot. Devlin - the murderer - turns up unannounced and uninvited. How did Devlin explain that he knew where the victim was staying when he was murdered? Media reports might have mentioned the name of the hotel but there is no way they would have included the room number.
Plot hole: Well within earshot of the others in the small room, Curry comments to Heyes (purely for the viewers' benefit, since Heyes already knows it) that if Lom Trevors is killed, their amnesty will go with him. This information should have blown their cover, but for some strange (and unbelievable) reason, no one wonders what he's talking about. (00:19:00)
Plot hole: Lupin was captured by chance, and he did not plan for that, nor he seemed to have previous knowledge of Stern's appearance, but he escapes regardless using a Mission Impossible-like perfect mask of him. He also somehow kept his own blazer, tie and shoes underneath the uniform and boots he stole and wore. (00:16:00)