Continuity mistake: When Columbo meets Goldie for the first time she is having a massage. She then proceeds to dress by tying a dressing gown with a bow at the front. In the next shot the dressing gown is open with the tie at the back.
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.
Continuity mistake: Colombo is talking to Mr. Kingston in the building entry after the reading of the will. A girl with red and white striped sleeves walks out of the building. A minute later she walks out of the building again. (01:15:50)
Continuity mistake: Just before the end we see a slide of Columbo looking at the lamp, but in the next shot of Columbo the slide is reversed.
An Exercise in Fatality - S4-E1
Plot hole: When Columbo finds Stafford's street shoes in his locker, they are tied. How did Janus get his shoes off without untying them? If Janus did untie them, why did he retie them before putting them in the locker? And why didn't Columbo wonder why someone would take off his shoes and tie them before putting them away?
Suggested correction: I'm not sure how this is a mistake. I always take my shoes off without untying them.
I can't take off my lace shoes without untying them. How do you do it?
Guessing by them not being tied too tightly. Depends entirely on how much give is in the shoes or the laces - it's certainly not unreasonable.
A Bird in the Hand... - S11-E3
Factual error: They are watching a football game on TV with The Stallions playing some other team. The game they are watching is actually a Canadian Football League game between the Edmonton Eskimos and the Saskatchewan Roughriders.
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?
Continuity mistake: When Columbo confronts Markham in the lecture hall and helps him erase the chalk board, most of the word "architecture" remains, visible over Columbo's shoulder. In the next shot, it disappears. (00:31:00)
Double Shock - S2-E8
Continuity mistake: Columbo stands in the doorway of Lisa's balcony while he questions her, and her gold drapery catches and hangs over his right shoulder, where it remains in all the close-ups. When the shot cuts, the drapery is no longer caught on his shoulder, but is safely folded against the wall behind him. (00:32:00)