During the discussion the Club has while sitting on the floor, Claire's hairstyle changes back and forth from one shot to the next.
While Bender is crawling through the ceiling, you can see the chain for his wallet while he's crawling in both directions (flipped shot); the first scene his lips are moving (telling his joke), the second scene, they are not moving.
After Claire puts on her lipstick, she puts the cap on and puts it in her purse. In the next shot, it is in her hands again, and then she puts it away a second time.
The clock in the library changes during the same scenes throughout the movie.
When the principal and Carl are talking in the filing room, the label card on the file drawer is slanted up and sideways. In the next shot it is perfectly down, then switches back to up and slanted.
When the kids are let out of detention at 4:00pm you could see the sun is starting to set. However, in northeast Illinois the sun sets around 5:30pm in late March.
In the end credits, "Illinois Film Commission" is misspelled "Illinois Film Comission."
Bender is crawling through the ceiling which is a drop ceiling. Ceiling tiles are typically made of mineral wool, fiberglass, gypsum, perlite, clay, cellulose or starch and are held up by a grid of aluminum rails and steel wires. The grid can hold weight but not the weight of a person.
If Andrew had a dual meet on the coming weekend he would have been trying to manage his weight and not eaten the type of lunch that he had in the lunch scene.
Bender gets detention for apparently pulling the fire alarm. Pulling the fire alarm for a hoax is a serious offense and the punishment would be being suspended or expelled from school. Likewise Brian setting off a flare would also result in being kicked out of school. Plus both characters would actually be arrested for committing these crimes.
Throughout the movie it appears that Bender is wearing Claire's diamond earring in his left ear, even though she doesn't give it to him until the very end of the film. However, it is actually an ear cuff that is worn anywhere above the earlobe on the outer part of the ear. It is clearly seen when he puts on her earring.
When the kids are running through the halls of the school, they run past a window that seemingly reveals it is dark outside. In actual fact, they are running past doors leading into classrooms, in which the lights are turned off because it is the weekend.
When Andrew is doing his crazy dance scene in the Library after getting high he jumps through the Georgia State Flag (the Confederate Battle Flag) a couple times.The High School is in Illinois though. The flag may have been in there for historical purposes; the Civil War and the Confederacy are common study material in a high school history curriculum.
The reasons Bender, Andy and Brian were in detention (pulling the fire alarm, assault and having a gun at school respectively) would typically warrant them being expelled at most schools. In a modern school this is certainly true, but the film came out in 1985, when attitudes towards these activities would have been strict, but more lax than those of the modern era. Additionally, Brian brought a flare gun, not a handgun that could have killed or injured someone.
In the beginning of the movie Bender has two matching shoes, in the gym he has one white shoe and one black. In that same scene he loses one shoe, but a scene later he has two matching shoes again. This is because he's stolen a pair of shoes and only puts one on, then later the other.
When Bender is ripping pages out of books the pages are blank but when he throws the book at Brian you can see some pages have pictures and writing on them as they fall to the ground.
At the end of the film when Brian was writing the essay/letter, he kisses the paper. There is nothing written on the paper.
On a far wall, in the school library, there is a magazine rack and bookshelf that reads "Librarians Selections." This is grammatically incorrect, as it is possessive and should read "Librarian's Selections."
Andrew's last name is spelled differently twice. In the beginning of the movie, a newspaper clipping spells it "Clarke." However, in the end credits, it is spelled "Clark."
When Vernon is attempting (and failing) to force the library doors to stay open you can clearly see that each door has a built-in stopper at the bottom.
Both Claire and Andy have lunches that require refrigeration. Claire with sushi and Andy with a carton of milk. Both of these sitting in a warm library for hours on end would make the consumers sick.
The kids for some reason don't know each other while in detention. Given how they all obviously go to the same school this should be impossible because while they may not know each other personally they should have met each other on a day to day basis at school.
It is very strongly implied Allison was the only teenager who had no reason to be in detention. Dick Vernon the vice principal should had realized there was an extra person in detention and tell her she shouldn't be there. And he even hands her a sheet of paper and a pencil, when he should only be expecting 4 people in detention, not 5.