Other mistake: Columbo never told the character Graham McVeigh that he was sick from clams. When Columbo came to the horse track to talk to him about the case, McVeigh said to Columbo "not more clams?" when Columbo said he was sick again.
Visible crew/equipment: When Fortelli threatens Graham, Fortelli says, "I don't want the money; I want the farm," and just as he adds, "I'll see you at 6:00 tomorrow night," we can see the reflection of the moving boom pole/mic on the vehicle's window. (01:02:50)
Visible crew/equipment: After Columbo searches the victim's car and has Brindle bag a few things, Columbo heads out with his bottle of Pepto Bismol. It then cuts to Graham at the stables, and as he and Pat turn left, we can see the reflection of the lighting scrim on the door's glass windows. (00:24:15)
Visible crew/equipment: At the start, while Graham is driving he makes a right turn, and as the van passes the camera, the reflection of the scrim diffuser, etc, is visible on the van's surface and windows. (00:00:20)
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