At one point in the film Jamal mentions to Claire that, "It was Stamford... At the bar in London... He was the one who introduced Watson to Holmes", alluding to the Sherlock Holmes novels and stories. However, it wasn't at a bar in London where Stamford introduced Watson to Holmes but at a hospital's chemical laboratory near the bar.
In the basketball state championship, the opposing team scores, and then Mailer calls a time out. During the time out, the coach says "if we get a stop here, they'll have to put us on the line", yet Mailer should have had possession, thereby not necessitating a "stop".
When Jamal is talking with the BMW owner, Jamal makes the statement about the origin of the BMW logo representing spinning propellers. This is actually not true. The BMW emblem is actually derived from the national colors of Bavaria and the roundel was mirroring the original Rapp Motor Works emblem.
In the basketball championship game played at Madison Square Garden, the three point lines are clearly NBA distance, but in high school competition, the distance of the lines should be about four feet closer to the basket.
During the close up of the typewriter, the letters should appear on the page as the letters are struck. But all the words are already on the page and just scroll across rather than get created as they are typed.
At one point, William Forrester chides Jamal about "The single most important criteria" of writing. Given how precise his character is about language, it is unlikely that he would use the plural (criteria) instead of the singular (criterion) - (although after leading with the tautological cliché, "the single most important", perhaps linguistic clumsiness is only to be expected).