Seth wears a shirt during the basketball game featuring the number 88. This is a Nazi skinhead code for HH, or "Heil Hitler," H being the 8th letter of the alphabet. It also refers to a set of 88 precepts written by the neo-nazi leader David Lane. The 88 precepts are rules and concepts that all White Supremacists lived by.
The diner that Danny and Derek go to get breakfast at before Danny goes to school in the morning is the same diner that is used in The Big Lebowski (1998), during the infamous "toe" scene. It's located at Wilshire and Fairfax in Los Angeles and is called Johnie's Coffee Shop and is only open for filming.
The punk band Anti-Heroes sued New Line Cinema over a character's tattoo featuring the band. The band did not want to be associated with Nazis, even fictional ones, in any way. The band went on to record a song called "NLC" that debases the film studio.
Edward Norton was said to have re-edited the film to lengthen his screen time. Director Tony Kaye then attempted to get his own name removed from the credits but violated a Directors' Guild of America rule that states that directors that use pseudonyms (such as "Alan Smithee") must not talk about why they had their name removed - which Tony Kaye had done in ads in Variety. According to Entertainment Weekly, he then wanted his credit to read "Humpty Dumpty". Eventually, Kaye sued the DGA and New Line Cinema for $200 million ($275 according to the book Cinematic Century) stating that the DGA rule violated his first amendment rights.
One of the T-shirts that Seth wears late in the film (when he is at the party at 57:33) that says 'Skrewdriver Rising' printed on it. Skrewdriver was a British white power skinhead band which lasted from 1976 through 1979 and again from 1982 through 1993.
In the midst of the dispute about the time he was taking to edit the film, Director Tony Kaye attended a meeting with Michael De Luca (then New Line's senior product president). Kaye arranged for a Jewish Rabbi, a Catholic priest and a Buddhist monk to be present at the meeting to support his argument and "make the meeting a more spiritual one".
The trivia items below may give away important plot points.
The original ending was of Derek standing in front of a mirror, shaving his head after Danny was shot. This was to make sense of the endless cycle of violence and tie the otherwise disjointed plot together but was removed after Edward Norton objected.