Columbo gets visible white cat hair all over his gray trousers when he momentarily kneels near the victim's body. However, moments later, Kinsey shows no trace of cat hair on his black trousers after crawling extensively across the same area.
When Columbo asks the female conspirator if she wants to talk to the DA, he indicates that the DA is a woman, saying that "she" is in the judge's chambers and that if "she" isn't, those in the judge's chamber would know where to find "her". A few minutes later, though, the police officer accompanying the woman to whom Columbo had said this yells across the street to Columbo that she had contacted the DA and that "he" was available and that they were going up to see "him".
When Columbo and Patrick are in the meeting with the Calverts and the lawyer, Columbo quietly picks up a cigar in the ashtray and slips it into the left pocket of his overcoat. When Columbo steps off the elevator after the meeting, he pulls the cigar out of his right pocket.
While Mrs. Calvert is sitting in the passenger seat of the police that is parked outside the courthouse, Columbo approaches. Mrs. Calvert exits the vehicle, and the passenger window is rolled up; however, in the next shot, the window is rolled down.
When Columbo shows up at the murder scene, he offers a banana to his colleague, who accepts it and takes a bite. Moments later in a closer shot, the banana remains unbitten.
The ashes that are poured out of the urn look like ashes from a barbecue pit. Human ashes do not look like actual ashes even though they are called ashes.
Clifford punches Seltzer in the ballroom, but his wife tells her lover, Kinsley, that he punched him down the stairs. There were in fact 1-2 steps in the room where the assault takes place.
When they are outside the courthouse they are clearly on a 2 way street that is made to look like a 1 way street. Mrs Calvert's car is parked on the wrong side of the road. Traffic is only going one way on a 4 lane road with all traffic in the right 2 lanes. You can see a bus in the background that is parked in the right direction. Every car that passes Columbo while he is talking to Pat has made a right turn from the previous cross street. No cars come from any farther up the street.
(At around 29 mins) A shadow of the boom mic is visible in the upper left frame.
When Patrick Kinsley and Columbo are at Howard Seltzer's house for the second time, the cat discloses the missing cigar cut. Patrick tells Columbo, he came back to find the cigar cut. Only the murderer could have known there was a cigar cut in the ashtray, since the cat dragged it out before any investigators appeared. Columbo could have suspected Patrick right there.
There is no indication, explanation, or reason for why Cathleen doesn't tell Pat or give Pat a wedge cutter for the cigar or cut the cigar prior to giving to Pat, since she would have known exactly how her husband cuts them as he was very particular, and she is the one who gave Pat the cigar to plant.
Patrick should have known that one of the more important pieces of forensic evidence is photographic either of the forensic officer or of witnesses. Therefore it seems dumb to plan the kind of murder where a picture of Mr. Calvert before Cathleen was able to plant the cat hairs would be very difficult to prevent or control especially at an event where hundreds of pictures would be taken.
When Columbo is told that the emergency contact on the victim's alarm contract is his attorney "Tracy Rose", he asks if anyone has been in contact with "her". However, he has no reason to assume "Tracy" refers to a female attorney, unless he knows her, and when they later meet, it's clear that neither knows the other.
Near the end, when Columbo is at Barney's, he is smoking his cigar, yet there's a No Smoking sticker on the door.