A Deadly State of Mind - S4-E6
Plot hole: Collier damages a post with his car as he leaves the driveway. His car would certainly have been damaged. The storyline is not long enough for Collier to have his car repaired. Columbo knows about the damaged post, but he never looks into how the damage occurred and never looks at Collier's car, which would have been incriminating.
A Deadly State of Mind - S4-E6
Plot hole: Collier's relationship with Nadia Donner is wildly improper, and her husband knows about it. It seems unlikely that nothing was done about it.
A Deadly State of Mind - S4-E6
Plot hole: (Spoiler) Mrs. Donner screams in fright just as she jumps to her death from her balcony. This seems unreasonable since she believes herself to be going for a swim (under post-hypnotic suggestion) The scream is heard by a later witness to help establish time of death. If she suddenly realized the deadliness of her act, why would she continue with it?
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