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)
Character mistake: Tina Fey fumbles her line and has to start it again. The original line should have been "How long do you think you're going to get away with this? Hazel or Jenna will know we're missing." Instead the second part of the line is "Henna or Jay; Hazel or Jenna will know we're missing!" (00:04:05)
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)
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.)
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.
Revealing mistake: In an early episode Jack introduces Tracey to all the TGS writers, but giving mini bios and facts about them in rapid Succession. Seconds later we go to a flashback of Jack's assistant holding up pictures of random people as Jack names them. The problem though is you can see that it's the same picture being used every time.
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.