The movie continually updates the time of year. But in the portion of the year labeled "September", the leaves on the trees are all red and gold and falling off. In "October", however, the trees are completely covered with green leaves.
When Mr. Blume is on the diving board there is a shot looking down on him and his cigarette is very close to burned up; but in the next shot he has almost half a cigarette left.
In the elevator, Max and Mr. Blume swap their position.
When Rosemary Cross was talking with Max in her classroom after leaving her job, the students' artwork she previously had taken down just seconds before in the same scene reappears.
When Max is riding the replacement bicycle to Blume's work to sabotage his car, the rack on the back of the bike has nothing in it; when he gets to the gate and rides in, there is now a small pack attached to the rack (from which he pulls his tools in the next scene under the car).
During the math class, the board is shown. y = f(x) = x^0.5. The question is to compute f(x+ deltax) - f(x). The first statement is accurate. The second statement is obtained by multiplying by 1 in the form of [(x+ deltax)^ 0.5 + x^ 0.5]/[(x+ deltax)^ 0.5 + x^ 0.5]. Thus the denominator of the second statement should be [(x+ deltax)^ 0.5 + x^ 0.5], NOT [(x+ deltax) + x^ 0.5]^0.5 as shown on the board. Interestingly, the third statement on the board has the denominator correct.
In the end credits musical listings, the name Jeremy (of Chad and Jeremy, who contributed 'A Summer Song' to the soundtrack) is misspelled as Jeremey.
When one the Blume twins get into their father's Bentley after school, one of them turns up the air conditioning. The automatic heater controls shown are not the same as those in the Bentley, which has manual controls. The controls are from a Mercedes-Benz C-Class 1994 or 1995 model year.
The supposedly unsolvable math problem appearing in Max' dream sequence is to prove that the area of an ellipse with semi-major axis a, and semi-minor axis b equals (pi)ab, which is a routine calculus problem, and not ridiculously hard.
At one point a reporter is interviewing Max Fischer with a tape recorder. As he's holding it up to Max to speak into, it is very obvious that the tape recorder is not moving, the wheels inside are at a standstill.
When Magnus confronts Dirk and tells him about what Max said he did with Dirk's mom, a crew member is reflected in the window behind Dirk.
When Max goes to meet Blume's wife, the camera and crew are reflected in the building behind them.
When Max is thrown within the first couple of seconds of his wrestling match, the outline of his stunt pad is clearly visible in the back of his singlet.
When Max and Mr. Blume are walking outside Max' father's barbershop, crew members can be seen in store windows.
The Swiss Army Knife Dirk gives Max says "Rushmore Yankee 1985-1997". Since Max is 15, this would mean he has gone to Rushmore since age three. But his first talk with Dr. Guggenheim reveals that he has only gone to Rushmore since second grade.
When Mr. and Mrs. Yang meet Mrs. Whitney at the play, they ask, "Are you Mrs. Whitney, the English teacher?" She says "Yes" despite the fact that she is the math teacher.
Ms. Cross says, "These were just born", referring to a tank of full-grown neon tetras.
In the first close-up shot, the box with the "Perfect Attendance" and "Punctuality Award" pins appear from left to right. But when Max reads out the names of the pins (in the same order as above), he points at them from right to left.
When Max is shown in the Model UN delegation as "Russia", he has an old, red Soviet Union flag on his desk (note the hammer and sickle), although the USSR fell in 1991. A closeup of Max's Swiss Army knife reveals that the story takes place in 1997, by which time the current white, blue, and red Russian flag was adopted.