Audio problem: When the Spring Fling Queen nominations are being announced applause can be heard for both Janis and Cady but no one in the class is clapping.
Continuity mistake: When Regina is talking to Cady about Janis, Cady is wearing a light blue ribbon in her hair. As the scenes cut in and out of Cady the ribbon changes from front to back a few times.
Other mistake: The layout of the cafeteria is different to that of Jamis' drawing. The position of several of the groups is wrong in relation to other groups. Even though the camera pans round quickly, it's easy to see that they don't match. Also, the drawing shows the "fat girls," etc. being on the back row next to a wall, but there's another row behind them.
Other mistake: When Cady gets back her test (the one scored with a 98) from Ms. Norbury, the date on the test is October 14th, 2003. However, that scene is set after winter break. (00:45:30)
Revealing mistake: When Aaron and Cady first speak and you can only see the back of Cady, you can tell it's not Lindsey Lohan because it is a messy, red wig and again after Aaron asks her for a pencil, you can still tell it's not Lindsey Lohan.
Answer: Regina enjoys manipulating people, and she views Cady as a relatively easy person to manipulate, finding her more useful/amusing to keep in their circle. It's a running theme of the film that the friendships between all of the Plastics is very tenuous, because of the catty, manipulative nature of the girls.
Purple_Girl
Also, if Regina tried to ban Cady, people might think she was threatened by Cady. Better to keep Cady around and attack her in subtle, manipulative ways.