The first time when Pierre is in Augustine's office, he mentions the pictures of students on the wall. During the shot of the students, the pictures of Rock's brother and of LaRhette's brother are side by side. But when Pierre asks Augustine about Rock and LaRhette, she points out the students on the wall but LaRhette's brother's picture is below Rock's brother's picture.
When Morgan comes to the school to dance with Pierre for the students, she descends the steps to the room fully costumed, including her shoes. Ballroom dance shoes have soft suede soles that are are easily damaged by wet or dirty floors, so most dancers, especially serious ones like Morgan, will not put risk their shoes by putting them on at a non-competition venue until they are ready to step onto the dancing surface.
In the dance scene with Pierre and Morgan during the detention, they dance Argentine tango, which is not considered a ballroom dance. American and international tango, both ballroom dances, are completely different.
Since the students in Pierre's class had never competed before, they would be automatically in the newcomer category, whereas the students from Pierre's studio would be competing at higher levels of bronze, silver, gold or open syllabus. Also, the students would be disqualified from dancing moves that were non-newcomer/bronze syllabus, which several of them did.
After Mr. Temple's first argument with Augustine about detention, he leaves the main office and forcibly closes the door behind him. As the door closes, the supposedly solid structural wall shakes noticeably.