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.)
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.