Backed by the Pentagon: Well, by the LAPD in this case. Actual SWAT officers appeared in the opening scenes of the movie, most of them in delivering the hotline between the negotiators and the bank robbers.
Throw It In!: The brief shot of Street vomiting after working out was something Colin Farrell came up with on his own. He told director Clark Johnson that he had a good idea for a shot, asked that a camera be set up, ran to craft services to get a mouthful of soup, and dramatically spit it out when the camera was rolling.
Unintentional Period Piece: The film came out in Fall 2003, right at the height of the Bush era — and it shows. Tellingly, the villain is a thoroughly despicable French criminal who's repeatedly subjected to anti-French epithets (back when the French were still Acceptable Targets because they opposed the invasion of Iraq), while the Latina Token Girl on the S.W.A.T. team is called "J. Lo" at least once (back when Jennifer Lopez was still a household name, and before Gigli put her career on the decline). But far more telling is the portrayal of the rough-and-tumble methods used by the S.W.A.T. team. LL Cool J's character bashes a civilian for her "liberal" views after she dares to criticize him for roughing up an African-American perp in South Central, and there's an extended scene where the two main characters mock a S.W.A.T. candidate because he's never had a civilian complaint against him, and prides himself on handling every past situation nonviolently. Considering the large-scale controversy and protests against Police Brutality and the militarization of police in The New '10s, which made police reform a hot-button issue, these scenes couldn't possibly have passed a test audience a decade later.
Paul Walker could have been Jim Street, but his commitments to the Fast and the Furious franchise kept him from doing so. The role was also considered for Mark Wahlberg.
For the scene with the Learjet shootout, the Sixth Street Bridge in Los Angeles was closed for filming. Just by chance, a high speed chase involving a stolen vehicle actually drove through as the cast was rehearsing the scene. At the time, the Learjet was parked on the bridge in such a way that there was just barely enough room for a mid-sized car to fit through, with a few inches of clearance on each side. At first, when the crew was told that a chase was headed their way, they thought it was a joke until they noticed the LAPD and news choppers above them. The crew tried to include the footage they got later from the choppers into the movie, but it didn't work too well.
The bank robbery used in the opening shootout was an abandoned building scheduled for demolition, so the film crew was allowed to shoot at it, tear it apart and do whatever they wanted to. They also had to get over 500 signatures from residents and businesses for permission to fly the helicopters at low altitudes for the scenes with Gamble, Street and the others being deposited on the roof.
The officers who deliver the secure phone to the hostage takers in the opening bank robbery sequences were actual LAPD SWAT officers who were on the set as technical advisors, and got a chance to put on their uniforms and do it "for fun".