Crew or equipment visible
Errors in geography
Elizabeth receives her admission letter to Harvard in October, before Halloween. (The party she and Donnie have is a Halloween party to celebrate her admission.) However, Harvard belongs to the universities that use the universal application and notification dates: applications have to be received by Januay 1 and letters of acceptance (or rejection) are mailed on April 15. To be coherent with Harvard's system, the film would have to take place in April, not October.
Incorrectly regarded as goofs
The movie is set in 1988, but license plates, book editions, news photographs and products from 1989-1999 appear throughout. These anachronisms fit in with the movie's themes of time travel and altered realities. (Chapter 4 even mentions how things from the future, such as Mayans having arrow heads, are symbols of future being brought to the past - these anachronisms are on purpose.)
The name of the high school is "Middlesex," which would obviously be abbreviated "MHS" for Middlesex High School. Immediately before Donnie's time travel conversation with his teacher, we see the top of the entrance of the school. There is a stone cross there with the letters "IHS". However, "IHS" is catholic acronym from Greek name of Jesus (Ihsous) and is commonly placed on the crosses. This letters aren't supposed to be acronym for the name of the school.