Continuity mistake: When the boys are sneaking in to take the pictures of Payne, the first time you see him in bed the clock says it's 4-something. When they come back and get the boy in the dress in the bed, the clock says 12-something.
Continuity mistake: When Major Payne screams while telling the story of the little engine that could, the wide shot shows that his hand is on his chair. The close-up however shows that he's sticking his hand out.
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.
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