Continuity mistake: Columbo wears a tuxedo the entire episode. Hours after his nephew's wedding ceremony, when Columbo's at the police station investigating the bride's abduction, his bow tie is hanging loosely around his neck. Shortly after, as he and the other detectives rush to the photography studio, the bow is now properly tied. This situation was too dire to bother redoing it, nor does Columbo ever worry about his appearance.
Other mistake: When Melissa sends Andy to have a shower we see that there are several sets of clothing in the closet. We see them again in her flashback when she awakes after being kidnapped. They have just arrived in the Bridal (Empire) Suite, and are leaving very early the next morning for their honeymoon. Why would those clothes be in the closet?
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