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)
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