Bums: Making a Mess All Over the City - S3-E14
Continuity mistake: When Frank, Charlie, and Dennis are in the cop car at the red light, they're on a one-way street, with cars parked to their left (facing the same direction as the cop car). However, when it cuts to Frank, we see a car drive by in the opposite direction, and the parked cars are gone.
The Gang Gets Held Hostage - S3-E4
Continuity mistake: When Frank and Charlie are coming out of the vent and onto the roof there is no gun taped to his upper back, he walks up to the Mcpoyles and a gun is magically taped there. (00:19:40)
The Gang Gets Held Hostage - S3-E4
Revealing mistake: When Liam is stabbed in the arm, as he turns around to walk away, you can see the outline of his real arm wrapped behind his back, under his robe for about one full second, revealing that the arm he was stabbed in was a fake prop-arm.
Mac is a Serial Killer - S3-E10
Plot hole: Early in the episode, it is mentioned that the serial killer is murdering "Young, attractive blondes", yet at the end of the episode, when the gang finds all the severed heads in the killer's refrigerator, almost none of them are blonde or young, contradicting what had been previously established.
Bums: Making a Mess All Over the City - S3-E14
Factual error: Charlie drops the moltov cocktail into the police car in the end, light enough so that it doesn't break, but the car explodes about ten seconds later, as Charlie explains he had soaked the entire inside with gasoline. However, there realistically wouldn't be such a long pause as shown in the show for the gasoline fumes to ignite. Also, the explosion is much more powerful than it realistically would have been, revealing pyrotechnics were used. Obviously done for comedic value, but still a mistake.
The Gang Gets Invincible - S3-E2
Continuity mistake: When Mac and Dennis are talking to Doyle on the bus, watch the background outside of the window. Every time the camera cuts back and forth, the background changes. The most noticeable change is near the end of the scene, when the background changes from trees and shops passing, to suddenly the side of a bridge passing.
Bums: Making a Mess All Over the City - S3-E14
Continuity mistake: At the end of the episode, when Charlie leaves the envelope marked "4 the Mare" outside the Municipal Building, as he walks away we see a janitor come by and throw the envelope away. However, seconds later when Charlie jumps into the air, we see the janitor walk and bend to pick up the envelope again.
Dennis Looks Like a Registered Sex Offender - S3-E11
Continuity mistake: After Mac's dad crosses the first name off the list, he folds the paper back up and caps the sharpie. In the next shot, he's folding the paper and capping the sharpie again.
Bums: Making a Mess All Over the City - S3-E14
Continuity mistake: When we see the cop car, none of the black panels have markings on them. When we see the car burning at the end, the rear black panels have markings on them.
Dennis and Dee's Mom is Dead - S3-E3
Continuity mistake: At the beginning, when we first see Dee, her tray doesn't have any bottles on it, but in the next shot, she now has at least 2 bottles on the tray (next shot we see 3) from cleaning up that should wouldn't have had time to pick up.
The Gang Gets Invincible - S3-E2
Continuity mistake: At the start Charlie's fairly clean-shaven, then when they all sit in the park after agreeing to get some fresh air, he's got his usual beard / heavy stubble.
The Gang Gets Invincible - S3-E2
Visible crew/equipment: When Frank is in the bathroom, we can see a part of the cameraman shirt. (00:14:30)
The Gang Solves the North Korea Situation - S3-E6
Continuity mistake: When Mac walks in with the duster, the red ashtray on the bar is sitting flat. When Dee is stating "That parts simply not true," the ash tray is fallen at an angle, it switches back to flat when Dennis joins the conversation, and then back to an angle when Frank tells the gang it's the North Koreans. Then it's back to flat one more time before the opening credits. (00:00:40 - 00:01:50)
The Gang Solves the North Korea Situation - S3-E6
Continuity mistake: Sun-Li disappears when the camera angle changes. (00:20:58)
Mac is a Serial Killer - S3-E10
Continuity mistake: When Dee is explaining that her and Dennis are going to just take the tools because her neighbor Gary is in love with her, Dee's hands are empty. When the shot switches to Dennis saying, "That works," she has a big silver wrench. (00:11:25)
The Gang Gets Invincible - S3-E2
Revealing mistake: When Dennis is running in slow-mo to catch a pass, the QB throwing him the ball is visibly in the background the whole time and never actually throws the pass. (00:16:00)
