Other mistake: When Josh and Cher are driving home from a party, they show a shot of the car. It's a blue sports car that passes a Hertz car rental sign. When Elton is driving Cher home from the party in the Valley, they show the exact same shot of the blue sports car passing the Hertz car rental sign.
Other mistake: On the back of the Clueless movie box, it says that it is "not easy being the most popular girl at Beverly Hills High..." but Cher goes to Bronson Alcott High School in the movie. The name is said and there are also a couple of scenes where you can see the initials BAH - most noticeably on the sweater of the gym teacher when Cher is trying to get her grade changed.
Other mistake: When Tai is at Cher's burning all the things that remind her of Elton, she talks about how she likes Josh and how he danced with her at the frat. They never go to a frat. According to Dicky Barrett of the Might Bosstones (band in the club scene), it was originally scripted to be a frat party, but the band refused that setting, so they chose a club setting instead. This frat reference (where Josh dances with her) is actually referencing the club scene.
Other mistake: Near the start when Cher asks Tai how old she is, Tai says, 'I'll be 16 in May.' Then Cher says, 'Well, my birthday is in April, so as someone older than you...' But throughout the movie it is said that Cher is already 16. No birthdays are shown. You'd think that a rich girl in Beverly Hills would celebrate her birthday.