Short Fuse - S1-E7
Continuity mistake: While riding in a chauffeur-driven car, Mr. Buckner wants to smoke a cigar. He picks up a wooden cigar box. The lid is secured by two pieces of black tape. He peels up one piece of tape. After a close-up of his face is shown, he peels up the second piece of tape and the first piece is now back in its original position across the lid.
Short Fuse - S1-E7
Continuity mistake: In the cable car climax, Roger opens the cable car door to throw out the cigars. Then while he is scrabbling on the floor, and there is dialogue, the doors are shut. Then, at the end, the doors are open again.
Short Fuse - S1-E7
Continuity mistake: When Buckner's car leaves the chemical plant, it's a stretch limo with three bench seats. When it explodes on the mountain road a few scenes later, it's only a two-seat limo. (Buckner, who was initially in the distant rear seat, is suddenly close enough to reach up and take the cigar box the chauffeur hands him from the front seat. The entire middle section of the limo has disappeared.) (00:13:40 - 00:15:30)
Short Fuse - S1-E7
Continuity mistake: As Roger helps Columbo remove the pink Silly-String from his hair, the amount and configuration of the string differs radically with each change of camera angle. (00:37:30)
Short Fuse - S1-E7
Continuity mistake: A chauffeur is driving Mr. Buckner to a mountain cabin. It is 7:30 pm and a very heavy rain is falling. The car explodes, killing both men. When their bodies are located the following morning, the road and the surrounding hills are completely dry. There are not even any puddles.
Short Fuse - S1-E7
Plot hole: We are told several times that the road to the mountain house is very narrow and difficult to negotiate. How did the very large crane get there so quickly to lift the bodies after the crash?
Answer: In the show, he was already a Lieutenant. A promotion would put him in the next rank up, which for the L.A.P.D. would be Captain. However, some of a Captain's duties would be overseeing other officers and ensuring they're compliant with policies, regulations, and standards. It would also most likely take him out of the field. This is something Columbo has no desire for as he rarely goes to police HQ's. Nor does he show interest in compliance and standards (for example, not going to his semi-annual evaluation at the firing range). However, he could still be assigned to a higher pay grade based on expertise, which is a form of promotion that does not include rank advancement. This would be going from Lieutenant I to Lieutenant II. I don't believe in the show it's ever started what his pay grade is. Although, in s02e01 (I believe) he mentions making $11K a year. Whether or not this was a true statement on his part, if you could find pay scale information for an LAPD Lieutenant in the 70's, it could give you an idea of his pay grade.
Bishop73