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.
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.
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.
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.
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.
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.
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.
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.