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.)
Answer: There's probably lots of reasons why Liz stays - money, lack of other job prospects and so on. The reality is, if she left, that would adversely affect the story line and the comedy within it. Tina Fey was one of the stars, and her character is an integral part of the show.
raywest ★