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.