Factual error: Despite the fact that other officers are doing so, Columbo does not wear gloves while examining the crime scene. He also eats and drinks in the room - both absolutely forbidden - leaving eggshells scattered about the place. The crime scene is now totally compromised and nothing found can be used as evidence.
Butterfly in Shades of Grey - S12-E2
Other mistake: Fielding Chase and Lieutenant Columbo are on a road in the mountains above Malibu and Chase's car will not start. He tries unsuccessfully to call the Automobile Club on his mobile phone. He tells Columbo the phone number is "555-4411" but each time he tries to call, he presses nine digits.
Butterfly in Shades of Grey - S12-E2
Continuity mistake: From his estate, Fielding Chase looks toward his front gate and sees smoke coming from the engine of Columbo's car. When we see Columbo standing atop the car and yelling for Chase to open the gate, there is no smoke.
Butterfly in Shades of Grey - S12-E2
Other mistake: Jerry Winters' mantel clock chimes four times but the clock shows the time as 3:59.
Undercover - S12-E3
Factual error: At the crime scene, the landlady of the dead man is brought into the room in order to identify one of the dead men. This is never, ever done - she could contaminate the crime scene in a dozen different ways. She would be asked to identify the corpse at the morgue after the scene had been cleared by forensic examiners.
Undercover - S12-E3
Continuity mistake: Columbo ushers Krutch and Susan into an office for questioning. When he closes the door, the venetian blinds on it change from straight to misaligned and back again between shots.
Undercover - S12-E3
Continuity mistake: When Krutch speaks to Columbo on the phone about 40 minutes into the show, his voice sounds like he has a cold. Earlier and later in the show, his voice doesn't sound like that.
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