When Rafe sets off the sprinkler system in the principal's office, the rest of the school has multi-colored dyes mixed in with the water, resulting in the students' hair and clothes, and building walls, being covered in many colors; however, the water coming from the sprinklers in the principal's office remains clear regular water, and Rafe and the principal's clothes never change colors. Furthermore, in the next scene, Rafe emerges from the school with his shirt covered in dye, though he was never exposed to the dye due to the goof in the principal's office.
When the monstrous school building says "B.L.A.A.R.!" you can see that it has a lower jaw, but when it pulls itself forward with its teeth, its entire lower jaw is gone.
The janitor Gus brings in a bucket of Hydrofluoric acid to disintegrate Rafe's book; however, the acid would actually be strong enough to burn through the bucket, presenting a hazard. The correct way to store hydrofluoric acid is to put it in a plastic container.
When Rafe puts a lighter to a sprinkler head in Principal Dwight's office, the entire sprinkler system in the entire school activates with colored water in the school hallways. Fire sprinklers do not all go off at once, only the one closest to the fire goes off.
The trophy case would not have the strength to endure the water pressure of the aquarium. Even if it did, the case wouldn't be watertight.
When the teacher draws a chart on the chalk board, you can see the eraser marks from where the chart was erased after prior takes of the scene.
The principal throws Rafe's journal in the bucket of acid causing it to splash on the sides. In a following shot, the bucket is perfectly clean.
Fire sprinkler systems are pressurized. When Rafe adds the dyes, he would have had to empty the system first. This would have triggered the fire alarm and dispatched the fire department to investigate.
When Georgia drives Bear's car, she hits several dumpsters. The dumpsters would not go straight up nor that high.
The school rules written down in Rafe's book change radically over time.
When Rafe first arrives at the school, the principal stops him for breaking rule 22 - the dress code; however, when Rafe goes into the school (and later into the classrooms) it is obvious that he is not the only student failing to comply with the dress code, as many of the other students are also wearing clothes that would violate rule 22. The principal, however, does not press on with the rule to the other students.