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.
Farewell My Beloved Witch - S1-E3
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)