The first scene in which Obi-Wan and Anakin appear was filmed after principal photography had finished. Ewan McGregor had shaven off his beard, so he had to wear a fake one.
Nearly every single Clone Trooper is computer generated.
In one of the trivia books about the movie, there is a page where the different beverages sold at Dex's Diner are illustrated. One of the substances is labelled 'Alludium PU-36.' Alludium PU-36 is the 'explosive space modulator' that Marvin the Martian attempted to use to blow up the earth in the Warner Brothers Bugs Bunny cartoon.
After the fight scene between Obi-Wan and Jango Fett at Kamino, as Jango runs up the walkway into his ship, the door closes from above and knocks Jango in the head as he enters. Deliberately done - a little nod to the Storm trooper in Star Wars. While there's no proof (yet) that all storm troopers are clones (films are the only canon, remember), this seems to suggest that a few years down the line at least some are, and have inherited their "father's" occasional clumsiness. Confirmed in the commentary.
The vehicle that Anakin steals for the Coruscant chase scene has deer whistles on it, right behind Anakin and Obi-Wan's heads. For those that don't know what deer whistles are, they are small whistles that mount on the bumper of your car and make a high-pitched noise (too high for human ears but perfect for animals) to scare deer off the highways.
Amidala seem to buy her suitcases on earth. I've owned the same kind of suitcase set used in the flick. They're from a company called "Atlantic". The only way they've been modified for the film is the funky padding inside. [If I remember right, it's this case she's using].
When Zam Wessel is killed by Jango Fett, her last words are in Huttese. What she says translates to "Bounty hunter slimeball."
The place where Padmé and Anakin walk on Naboo is the Plaza the Espana of Sevilla in Spain (you can see the same place in Lawrence of Arabia).
According to the DVD commentary, Anakin's shadow on Tatooine (before he leaves the Lars' to find Shmi) was not digitally altered to resemble Darth Vader's helmet. It was pure coincidence.
In the pursuit scene on Coruscant, when the two speeders are diving, you can see a X-Wing pursued by 3 TIE fighters in the ground's traffic.
The red aiming screen of Zam Wessel's binoculars is the same kind as that seen on the Millenium Falcon when the TIE fighters attack it after the escape from the Death Star in Episode IV.
The yellow speeder which Anakin takes to pursue Zam is inspired from the yellow Ford coupé 1932 of American Graffiti, another George Lucas movie.