When the students are in the classroom being questioned about cheating, Pearson (Rif Hutton) can be seen in the background capping his pen twice between shots.
When Mr. Escalante returns home after thinking his car has been stolen, the front windows are shown with their curtains closed. Once Angel shows up with his car, Escalante goes to the window to see what is happening, and the curtains are wide open.
When Angel is at the doctor with his grandma his tattoos on his hands are seen above his third knuckles on the backside of his hands, in the next scene when he returns to class the tattoos are back to being below the third knuckles.
The teacher in the classroom says Mayans were the first to contemplate and use the idea of zero. The first recorded zero appeared in Mesopotamia around 3 B.C. The Mayans invented it independently circa 4 A.D.
Jaime Escalante never had a heart attack as depicted in the movie. He had a inflammation of the gall bladder. He stated this in a interview.
When the class is shown in the movie at the calculus level, some of the problems written on the board and the lessons that Mr. Escalante is teaching are not calculus problems. They are Algebra II, Trigonometry, and Analytical Geometry, all prerequisites for Calculus.
When Edward James Olmos is taking out the garbage and makes a comment to his neighbor about how good his boat looks, the boat registration numbers are an Iowa registration not California where the story takes place.
The movie implies that Mr. Escalante taught the same group of students for several years from Algebra to Calculus. While he taught those subjects during his tenure at Garfield High School, he had different students throughout his teaching career. Using the same group of students for the movie was used to show how he could inspire his kids and make it easier for audiences to see their progress.
When Lupe is studying and her mother comes home from work, her mom asks her to turn off the lamp that is across the room. She is sleeping directly under a different lamp that doesn't seem to bother her.
In most of the classroom scenes, there are close-up images of the planet Uranus with two of its moons (Ariel and Miranda) posted in the back of the classroom. It would have been impossible for those pictures to be hanging in the classroom, because the events depicted in the movie take place between 1980 and 1982. The first time humans had close-up pictures of Uranus and its moons was when the Voyager 2 spacecraft flew past Uranus in 1986.
One of the students, while talking with Mr. Escalante outside, is holding a can of Diet Pepsi bearing the logo introduced in 1985, three years later than the movie takes place.
If Angel was concerned about his "homies" seeing him studying or whatever, why would he want a math book for his locker? One for the classroom and one for home should be suffice.