Keep the Home Fries Burning - S2-E14
Continuity mistake: When Andy and Kelso fight, Andy's right hand is either next to Kelso's armpit or his collarbone. (00:20:12)
Keep the Home Fries Burning - S2-E14
Continuity mistake: The sheriff shows the doctor the menu and cries, "His picture is all over the place!" Then he lays the menu down. A shot later, he is holding the menu with both hands.
Keep the Home Fries Burning - S2-E14
Continuity mistake: When the sheriff sits down at the restaurant table, Jessica's hands swap from lying on the table to raised.

One Good Bid Deserves a Murder - S2-E17
Visible crew/equipment: When Dr. Dunn is in Jessica's room, the boom mic is reflected in the mirror. (00:27:12)
One Good Bid Deserves a Murder - S2-E17
Continuity mistake: The first time Jessica is shown asking for her room number, she asks for room 812. Later in the episode she asks for room 810.
Plot hole: Barney Kale decides to reopen a case he couldn't solve. Based on the outcome it makes no logic whatsoever. He is the murderer. Why would he bring attention to it put himself in danger? (00:46:50)
Suggested correction: He was being blackmailed by Gary Roberts. He "reopened" the case as a ruse to kill Roberts.
Plot hole: There were 3 gunshots. 1 from Magnum, 1 from the killer and 1 from the victim. Yet they arrest Magnum with checking the bullet striations. He would be declared innocent almost immediately. (00:17:00)
Night of the Headless Horseman - S3-E11
Visible crew/equipment: When Nate and Dorian fight at the bar they are replaced with obvious stunt doubles with totally different hairstyles.
Night of the Headless Horseman - S3-E11
Continuity mistake: In the car, when Jessica is told that she has to act like Dorian's mother she covers her face with both hands. A shot later there's just one hand on her face.
Night of the Headless Horseman - S3-E11
Visible crew/equipment: When Jessica arrives at the station and Dorian opens the car door, stage lighting screens are reflected on the glass.
Night of the Headless Horseman - S3-E11
Visible crew/equipment: When Nate Findley rides his horse the actor's stunt is very noticeable in the wide shots.
The Corpse Flew First Class - S3-E12
Factual error: As the airplane is coming in to land at Heathrow, there is an establishing shot of the wheels down, and in the background there are cars on the road, but driving on the right, wrong for the UK.
Crossed Up - S3-E13
Continuity mistake: When the crime is solved Jessica shows her emergency calling button. The way she holds it changes between shots.
Crossed Up - S3-E13
Continuity mistake: When Grady grabs the diary it swaps between closed or open depending on the angle.
The Bottom Line Is Murder - S3-E15
Continuity mistake: When the cop picks up the dirty ashtray he blows the ash away. In the close-up the ashtray is spotless as if it had been wiped with a cloth or if it were brand-new. First of all, no ash blew away, and second of all, a mere puff couldn't have cleaned it the way it looks.
The Bottom Line Is Murder - S3-E15
Visible crew/equipment: When Jessica rides in the car for the first time, the structure of the filming equipment is reflected on the hood.
Factual error: The whole episode is run as if based in the UK, and yet the script has obviously been written by an American. The UK does not have autopsies, it has post-mortems. The UK does not have a trunk (of a car) it has a boot.
A Very Good Year for Murder - S4-E17
Visible crew/equipment: After Tony is cured he exits toward his car. A big screen used for lighting is reflected on the side of the car.
Plot hole: When Jessica is arrested for the murder of the enemy agent. Her purse is confiscated. It was reported stolen by Michael Haggerty. But throughout the whole show none of the cops looked at her ID. Besides that she's a famous women and someone at the police station would definitely know who she is.
Visible crew/equipment: When the sheriff and the mayor meet at the fix-it shop, the filming crew plus the boom mic pole are reflected on the side of the red car.