Why would the inventor of Toaster Strudels need to put his daughter in public school? Surely the resident Rich Bitch would be just one of many in some ritzy private academy?
Plenty of kids with rich parents go to public school. It might be because the parents do want to save money, (even if you're rich, a good private school is still expensive) though sometimes the kid goes to public school for the general environment. More exposure to different types of people and whatnot.
In some areas of the country, public school is just as good as (and just as expensive as, due to a combination of taxes and books) private school.
This movie was apparently set in the North Shore of Chicago, an area known for very wealthy residents and some of the best public schools in the nation. Private schools in that area are not significantly better than the public schools, and if the parents don't want to ship the children off to boarding school...it makes a great deal of sense that Gretchen goes to public school.
Why does Cady speak English with a perfect American accent when she's spent her entire life in Africa?
Cady didn't spend her whole life in Africa, just all of her School years. She could have been five or six when she when over, so english isn't a problem. As for the accent, she could have picked that up from her parents.
When she was in Africa she spoke the native language when talking to others. However she still spoke English with her parents at home. She learned how to speak English first and so she kept her accent from speaking with them.
Not exactly Fridge Horror, but if Janis choreographed the sexy Jingle Bell Rock dance when she was still friends with Regina, that means that she, Regina, and the other Plastics were no older than 12 or 13 years old when they started performing it at school talent shows (and presumably wearing the costumes).