According to producer/co-writer Dean Devlin, the U.S. military had agreed to support the film by allowing the crew to film at military bases, consulting the actors who have military roles, etc. However, after learning of the Area 51 references in the script, they withdrew their support.
(at around 1h 7 mins) The scene in which Will Smith drags the unconscious alien across the desert was filmed on the salt flats near Great Salt Lake in Utah. Smith's line, "And what the hell is that *smell*?" was unscripted. Great Salt Lake is home to tiny crustaceans called brine shrimp. When they die, the bodies sink to the bottom of the lake (which isn't very deep) and decompose. When the wind kicks up just right, the bottom mud is disturbed and the smell of millions of decaying brine shrimp can be very, very bad. Apparently, nobody warned Will.
Holds the record for most miniature model work to appear in one film. Model shop supervisor Michael Joyce estimated that more miniatures were used for this film than in any other two films combined. Due to the advances in digital technology since this film's release, most experts believe this record may stand forever.
Dean Devlin said that most of the dialogue in the scenes Jeff Goldblum shared with Judd Hirsch and Will Smith was improvised.
(at around 1h 45 mins) The President's speech was filmed on August 6, 1995 in front of an old airplane hangar that once housed the Enola Gay, which dropped the atomic bomb on Hiroshima exactly fifty years earlier on August 6, 1945. Interestingly, the crowd was not scripted to start cheering. Bill Pullman's delivery of the speech was so good that they just started applauding and cheering on their own and the filmmakers kept it in the movie.
Dean Devlin: (at around 2h) Producer and co-Writer is the voice of the fighter pilot alongside the President's plane who says, "I'm on it," targeting the alien ray only to be blasted out of the sky a moment later.
William Fay: (at around 39 mins) The co-Executive Producer can briefly be seen on the television in the Oval Office as a S.E.T.I. employee during the "Operation Welcome Wagon" scene.
Roland Emmerich: [Sky News] In any Roland Emmerich movie in which news broadcasts are depicted, his foreign news station of choice is SkyNews. Here, it appears in Russian. Sky News is owned by the News Corporation (now 21st Century Fox, Inc.), the same company that owns 20th Century Fox, which released this movie.
Roland Emmerich: [44] The number 44 is seen on the headrest in Russell's F-18 cockpit, several televisions are tuned to channel 44. When the ship above Area 51 is destroyed, just as it's falling to Earth, 44 can be seen in the flames on the side of the ship.