Revealing mistake: When Ms. Norbury spills coffee all over her shirt, you can see the hand that is to the left is pulling her shirt up with her sweater and rapidly lets go.
Revealing mistake: Regina writes comments about herself in the Burn Book, at the top of the page in red marker. Later, when Mr Duvall has the book, he opens it saying "Why would Regina refer to herself..." and he then looks at the page and reads "As a Fugly Slut?" However, watch as Mr Duvall opens the Burn Book - the page he has it opened at is blank at the top and there is no writing on it at all. (01:00:15 - 01:02:25)
Revealing mistake: In the scene where Mrs George is taking pictures of the girls for the Christmas concert you can see that the camera is turned off.
Revealing mistake: When the Plastics are walking down the hallway together, Cady falls into a trashcan. The trashcan stays upright, but it should tip over from the way she went in, the momentum and her bodyweight. Just a few shots prior to this, a janitor, on the left side of the screen, is seen moving that trash can, so it is apparent that it is not bolted to the ground. (00:44:00)
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.