Plot hole: Throughout the entire show, the chief, Juliet, and Lassiter constantly tell Gus and Shawn to stay out of their way and off their case. The chief even reminds them several times that they can't work on a case unless she's assigned it to them, ignoring the fact that Shawn and Gus are private detectives and do not need police permission to investigate a case.
Suggested correction: But they're only involved in police cases by invitation. People can't just take it on themselves to wade into crime scenes, private detectives or not. Warnings like that might not strictly be a command they "have" to obey, but it's in their best interest to take it on board and not annoy the department too much.
Woman Seeking Dead Husband - Smokers Okay, No Pets - S1-E4
Visible crew/equipment: When Shawn and Gus gets out of the car at the Mausoleum Parking, you can see the camera man reflected in the mirror inside the car.
Zero To Murder in Sixty Seconds - S2-E4
Continuity mistake: When Shawn and Gus find Johnny G's body in the car, he's slumped forward in the shots inside the car but slumped back in the shots seen through the windshield.
Other mistake: In this episode, Shawn supposedly impresses Jules at their first meeting by "divining" facts about her family and cats. We never hear about the cats again and later learn that her parents have not been together for 30 years.
Woman Seeking Dead Husband - Smokers Okay, No Pets - S1-E4
Visible crew/equipment: When Shawn and Gus gets out of the car to start digging for the money, you can see the boom mic reflected in the back window of the car.
Six Feet Under the Sea - S3-E10
Continuity mistake: As Shawn's dad is showing him how to drive the boat, he is alternately leaning against the railing with his arm outstretched, and with his arm at his side, depending on the camera angle. (00:20:25)
Psy vs. Psy - S2-E3
Revealing mistake: Whenever you see Shawn and Gus outside it appears to be warm but if you look in the background people are wearing jackets and heavy coats, revealing that during filming it was winter and cold out.
Continuity mistake: A man attacks the judge by running out of the shower. When he runs through the shower, a shower curtain is draped over him. For most of the scene it is over his head, but when he is dragging the judge into the shower, the curtain has moved off of his head and is even gone completely in one shot, perhaps to make the actor more visible.
Gus's Dad May Have Killed an Old Guy - S2-E10
Continuity mistake: Just before Shawn notices the abrasion on the corpse's scalp, the two men put the man's arm in the body bag and begin to zip it up. They then put the same arm in the body bag again, as the stain on the man's shirt front is shown.
Visible crew/equipment: S01E13 - "Game, Set. Murder?". When Shawn and Gus runs out of the crime scene apartment, heading for the restaurant across the street, you can see the camera and a crew member sitting on a chair reflected in the mirror behind Gus.
He Loves Me, He Loves Me Not, He Loves Me, Oops He's Dead - S1-E11
Factual error: Shawn reports that one of the attendees of the speed dating session drives a 2004 Trans-Am. The Trans-Am was discontinued in 2002.
If You're So Smart, Then Why Are You Dead? - S2-E7
Continuity mistake: When they are talking to the two kids outside of the school for the first time, one of the kids has a juice box. Shawn starts talking and it shows from behind the one kid with the juice box and he is about to take a sip, then the shot changes and the juice box is by his side.
Gus's Dad May Have Killed an Old Guy - S2-E10
Continuity mistake: The red ball in the first scene changes position. In the close up shot, there is a green plant in front of the ball with two stems. In the next shot (from above) there is no longer a plant on that side of the red ball.
Psy vs. Psy - S2-E3
Continuity mistake: When Shawn kicks over the carry-on bag at the end, it lands with the handle on top. The subsequent wide shot shows the bag with the handle on the bottom. The handle is back on top just before the bag is opened.
Continuity mistake: When Shawn, Gus, and Nigel are having dinner over at Henry's house, Shawn's plate already has a steak on it before Henry walks in with the first batch. Then, the steak disappears right before Henry plops one on Shawn's plate.
Other mistake: When Spencer is on the phone to O'Hara, his iPhone shows the standby screen, not the screen that comes up when you're talking to someone on the phone.
Continuity mistake: In the scene where Shawn is brought into his childhood bedroom to investigate Allison's abduction, there is a "Peeping Tom" band poster visible behind him for a few seconds. This was Shawn's bedroom in the 90's, and "Peeping Tom" didn't exist until 2006.
The Devil Is in the Details... And the Upstairs Bedroom - S4-E4
Continuity mistake: In one of the first shots showing Agatha's friend Lucy behind the police line, Gus is visible in the background talking before Shawn and Gus arrive at the scene. (00:03:20)
The Head, the Tail, the Whole Damn Episode - S4-E15
Visible crew/equipment: The scene where Gus is smelling for the first shark and Shawn is 'divining' it. As they round the corner at the dock, a camera and some randoms are visible down the alley for a few seconds. (00:19:00 - 00:23:50)
