Factual error: During the first few minutes of the film we see Major Payne report into the General. Major Payne then salutes, however, he does not have a cover on his head. As per USMC/Naval Customs and Courtesies, Marines only render the proper greeting of the day when reporting to a superior officer without a cover, they don't salute. (00:03:20)
Factual error: When Damon Wayans gives the nurse the bullet, explaining that he had removed it from his heart (presumably having been shot with it), the bullet is still whole, i.e. including the cartridge.
Factual error: When Payne is at the train station considering boarding it for Washington DC to return to active duty, it's a southbound train. The station he's in is Ashland, VA - DC is north from there.
Answer: Madison is not a military academy. It is a boarding school and Major Payne has been put in charge of their JROTC program. It is, however unlikely that those cadets, or the blind cadet at the end of the film, would be admitted into a JROTC program. The Code of Federal Regulations states that the JROTC program is designed for "physically fit" students. Tiger is also much too young to be allowed to participate, you must be in at least the 7th grade to participate. Madison is apparently making exceptions to allow basically anyone that wants to participate and that would not be allowed in real life.
BaconIsMyBFF