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 then the movie takes place.
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 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.
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.
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.