Factual error: An important plot point is that diamonds do not burn and can be recovered from the ashes of a cremated body. This is completely wrong - diamonds would combust freely at cremation temperatures, and since they are pure carbon they don't even leave any residue.
Factual error: In common with many other episodes neither Columbo, the attending police officers or forensic investigators wear gloves or other sterile gear while examining the murder victim's body or the crime scene. Columbo hands out bananas to other people on the scene which they happily eat. The senior crime scene forensics officer, Kingsley, hands out coffee and doughnuts! Eating and drinking are absolutely forbidden on a sterile crime scene, which has been hopelessly contaminated with fingerprints anyway.
Other mistake: Kingsley doesn't know if his victim is married or unmarried, whether or not he has children, if he has a maid, but he brings a hand vacuum and empty vial to the murder to collect cat hair from the victim's cat to plant on Clifford's jacket.
Murder with Too Many Notes - S13-E4
Other mistake: In the movie within the story the murderer repeatedly stabs the victim and pulls back the knife. Even after several stabs there is no blood on the knife.
Character mistake: Kingsley carries a briefcase in to the attorney's office, but leaves without it.
Continuity mistake: Close to the end when Colombo is talking to Patrick Kinsley he is holding up the bag with the cigar-end; the bag is upside down. In the next shot from behind the bag is the right way.
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