Character mistake: During the opening space battle, Obi-Wan's ship falls under attack by buzz-droids, who proceed to cut into his fighter, disabling a number of systems and leading Anakin to try some decidedly dangerous moves to get rid of them. Both Anakin and Obi-Wan are acknowledged experts in the use of the Force and both have been shown to use the Force routinely, even for relatively mundane activities. It's also been firmly established that the Force works on droids and that the Force-user can still affect others through windows, viewscreens and so forth. Yet neither thinks to use the Force to deal with the buzz-droids. (00:05:10)
Suggested correction: There's no evidence this is a mistake. In fact, it's logically self-defeating. As you noted, both Anakin and Obi-Wan are trained Jedi Knights. If the option of knocking the droids off with the Force was indeed feasible, presumably they would have done it. There are any number of reasons why they didn't (they couldn't concentrate enough in the middle of a pitched naval battle to commit a Force attack, the droids could have been attached magnetically, etc.) but the bottom line is that if telekinesis was an option they would have done it.
Character mistake: After the Lieutenant is shot and is in hospital, his CO is explaining what the GHOST system is. He explains that the acronym is "Guided High Altitude Scrambling Transmitter" - which would be GHAST. Replacing "altitude" for "orbit", which is probably what was intended, would make a Guided High Orbit Scrambling Transmitter - or the GHOST system henceforth referred to in the film. (00:06:25)
Character mistake: When Lt Gannon is in the dogfight with the Russian jets, he announces that he is deploying "chafe and flares." The term is spelled and pronounced "chaff", and any pilot would know that.
Character mistake: When the plane is speeding down the runway at the beginning, a female flight attendant is seen walking, and Kyle is seen buckling her seat belt. Everyone would have been sitting down and buckled in at this point.
Character mistake: When the Smiths first enter the store Home Made, the camera pans around and faces the store's large display picture which reads, "The true measure of a home lies in it's kitchen," but the word "it's" should be "its."
Character mistake: The bad guys at the beginning of the movie launch a drone that scans for target. The woman's data appears in the HUD and it says "Stacey Canon - Interpol REGISRTY" (00:02:20)