Continuity mistake: When Mac and Charlie are still on Ricky's porch after he's closed the door, Charlie's hands are empty. But in the wide shot when they're leaving, Charlie is now holding the robot, even though it's meant to be a continuous shot because there's no break in their conversation.
Continuity mistake: At the beginning, the position of Dennis holding his cigarette changes between shots. For example, when Dee says "thank you", Dennis is putting the cigarette down, and then in the next shot when Charlie walks in, Dennis has his hand back up and is putting the cigarette down again.
Other mistake: In the opening of this episode the screen reads "3:50pm On a Wednesday." When Gino (Frank's Brother) is reading the letters meant for Shadynasty, he says "Meet me at the airport, Friday, at 5:00, Terminal C." The gang and Gina then go along to the airport that very afternoon - a Wednesday - to try and meet Shadynasty and get her and Frank back together. And of course she is there, despite it being a Wednesday, not a Friday.
Continuity mistake: Dennis walks up to the computer to see the guy claiming to be their father carrying nothing, he puts his empty left hand on the bar, but when the shot switches he is holding a coffee in that hand. In the shot right before the opening credits the coffee is gone again. (00:01:00)
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.