The Gang Exploits the Mortgage Crisis - S5-E1
Continuity mistake: After Dennis, Charlie and Mac kick apart the family's front door, the amount of damage to the door decreases significantly when Frank begins questioning the lawyer.
Revealing mistake: During the training montage, right as Mac is about to smash the bottle over Charlie's head, you can see Charlie stop what he's doing about a half-second before being hit, and brace himself for the impact, despite not being able to see it coming. This is confirmed on the DVD commentary.
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.
Visible crew/equipment: During the scene where Dennis and the Waitress, Mac and Dee successively walk into the back office to talk to Charlie near the beginning of the episode, in some of the shots, you can see outside the office door, and you can see the top of the set has no ceiling, and even see part of a stage-light.
Continuity mistake: In the scene in the bar, when the lights go out, when they come back on, Dee's handbag is first seen on the floor in front of her. Then, in another shot, the bag is shown behind her. (00:15:03)
Dee Reynolds: Shaping America's Youth - S6-E9
Continuity mistake: In the final scene, in the principal's office, an orange magically appears on the desk in the middle of the scene. (00:20:08)
Revealing mistake: As Mac says "I'm very worried about these guys" and exits the bar, there's a shot right through the door and it's not the bar inside at all, just a wall with some pictures on it, much closer to the door than it should be.
The Gang Exploits the Mortgage Crisis - S5-E1
Visible crew/equipment: When the gang realizes the family is still residing in the home Frank has just purchased a verbal quarrel ensues, obviously. In one of the shots you can see a good bit of a crew member on the left side of the screen. (00:05:40)