Continuity mistake: In the psychiatrist's office, Columbo strikes a match and lights his cigar. Two seconds later, we switch to a closeup shot and the match is about six inches away from his cigar, which he proceeds to light again. (00:44:15)
Audio problem: There is a scene where the mistress of the murderer enters his bureau. You see her push the door closed while hastening through. You can hear the door lock click - but a half second too early. Her push wasn't that strong. (00:47:05)
Continuity mistake: At the very end Fleming sees the dead body of his girlfriend being hoisted onto a gurney - she is soaking wet, having been hauled out of the swimming pool. Later we see it is a policewoman acting as a stand-in in order to fool him into talking - and after a few minutes under a blanket on the gurney she, her bikini, and her hair are all bone dry. Not only that, her hair looks like it has just been styled and her makeup is perfect.
Character mistake: After Fleming has murdered his wife, he warns his girlfriend not to touch anything in the apartment, but he hands her a drink which he already prepared for her. At his direction she also makes a telephone call, holding the receiver with a cloth he hands her, but dialling the number with her bare fingers. On top of that, he hands her a pair of gloves after she has made the call - she would have touched or handled all sorts of things in the room by then. Why didn't he hand her the gloves as soon as she stepped in the room?
Suggested correction: This is a subtle hint that Fleming is preparing to frame his girlfriend for the murder. He would admit to having an affair with her (not a crime) but is going to deny any involvement in his wife's murder. (SPOLER ALERT!) Later he makes it clear that his girlfriend meant nothing to him and he didn't care that she had committed suicide (or so he thought).
Nowhere in the episode is this sub-plot explored or even mentioned.
Not only that, but the idea he was going to subtly frame his girlfriend doesn't make sense because he used her to establish his alibi. He tried to make it look like she was killed by an random intruder.
Revealing mistake: Just after the scene where the doctor asks Columbo to switch off the light before leaving, the detective does so, but it can be seen that both light switches are down before he does this, and that they are still both in the down position after he "switches off" the light.
Continuity mistake: When the girlfriend speaks to the cleaners the phone is on the bar, and then they leave for the airplane. When Mr. Fleming comes back the phone is on the table.
Continuity mistake: The chess set on the table is in a different position after the murderer returns from Acapulco as opposed to right before he murdered his wife.
Other mistake: Mrs. Petrie, Dr. Flemming's secretary, makes two phone calls to Joan Hudson. She dials seven numbers for the first call but only six numbers for the second call.
