Continuity mistake: In the episode "The Fighting Irish", Jack's brother and father appear. Jack says "I haven't seen my father in 17 years." But throughout the rest of the series, it is mentioned many times that Jack's father ran away when Jack was little.
Continuity mistake: In the pilot episode, when Liz walks back into the writer's office Frank throws a sandwich at her, and she tells them to get it out of their system, i.e. throw things at her. We see all of the writers (Frank, Lutz, Toofer, Josh, a bald man, and a woman) grab various items off the table and the female writer grabs what appears to be an orange ball. When the shot changes to the objects hitting Liz, the ball does not appear. (It is not the bag of Cheetos, as you can tell it is made of some kind of foam.)
Episode 210 - S2-E10
Continuity mistake: In the scene where Tracy is trying to get Kenneth to try coffee, watch the foam on the coffee. The foam decreases and increases throughout the scene.
Subway Hero - S2-E12
Continuity mistake: As Liz is talking to Dennis in the subway, he is leaning against one of the steel pillars with his left arm near to the location of his head. If you notice his arm is being supported by the pillar but his hand is not. In the shots of Liz whilst Dennis is leaning against the pillar, you cannot see his hand and the location of it should be covering part of his forehead.
Continuity mistake: When Kenneth is talking to Pete about his reference to a page in the Beijing Olympics, there is a bow and arrow that appears suddenly on the wall behind Pete that wasn't there in previous shots.
When It Rains, It Pours - S5-E2
Continuity mistake: When Liz flicks her cowboy hat at Pete he exclaims "you got sauce on me." When the scene starts Pete's shirt is clean. As Liz flicks her hat the camera points at Pete and there's already lots of sauce on his shirt, before one extra bit hits him. As Liz walks away and camera cuts back to Pete at the end of the scene and the extra sauce from the flick has gone.
Operation Righteous Cowboy Lightning - S5-E12
Continuity mistake: Jack walks into the writers' room. During a wide shot, you can see that Lutz has a pair of sunglasses resting on the back of his head, near his neck. During his close up, the sunglasses are gone. The next shot is another wide shot and the sunglasses reappear. (00:05:10)
Queen of Jordan 2: The Mystery of the Phantom Pooper - S6-E20
Continuity mistake: Liz is going to gives Virginia a book, but when she hands it to D'fwan in the next scene it's a plush giraffe. (00:10:40)
Suggested correction: Not a mistake, the joke is that the book is too loud for a TV show so they change it. You need to hear it in context.
