When Sykes and George are chasing Harcourt and Kipling in the police car as they push them off the freeway they are on the driver's side, in the very next scene, they are on the passenger side of the car.
During the shootout at the beginning of the film Kipling fires the 'BRI Sabot Slugs' at Tuck from his shotgun's drum magazine before he is seen loading the magazine in the first place.
When George drinks the milk at Matt's house the milk disappears from his lip between shots.
During the chase scene with the police car the tail lights on Sykes and Francisco's car change from broken to intact to broken again.
During the car chase when the criminals' car jumps the center curb while it's in the air the rear tire is seen and is twisted pointing 20 or 30 degrees towards the center of the car but after it lands they keep going and it is straight again. If it was damaged to where it was turned in like that the car would be unable to continue or would be swerving around and be very difficult to drive.
It is not possible for a human to flag down a helicopter by simply waving his hand, at night, from several hundred feet of altitude. The person is just a silent speck in the dark and all but invisible to the pilot.
When Sykes is about to be struck by Hubley's son at the bar, Francisco stops him. The son then says something in the Newcomer language that is translated on screen as, "You smell like a human". However, he is only saying Francisco's real name, the same one Francisco himself told Sykes earlier, not a statement about him smelling like a human.
When the computer operator retrieves the names of the four aliens, the results appear onscreen before she has finished typing.
When Sykes is about to return to his vehicle at the beach, his car is shown painted with an insult. It is implied that Fedorchuk and Altarez did it, but they were with Sykes the whole time he was at the beach so they couldn't have.
When Sykes slams Fedorchuk's face into the steering wheel, Fedorchuk is then shown with a bloody nose despite his nose never making contact with the steering wheel.
George's son is credited as George Jr., though he is named Richard in the film.
At the gun range, Sykes makes a speech to George about hunting down his partner's killer, then he turns and walks away. At this point James Caan forgets to take the gun. He then ad-libs, telling George to bring his gun.
When in their car, Sykes asks George for information on Hubley. At this point Patinkin opens a binder but instead of opening to the file, it opens to a closed folder, which is clearly in view of the camera. He then pauses, obviously thinking about faking it, then opens the folder and begins "reading" Hubley's information.
Matt's dialog doesn't match his lips after he and George talk to the hostess at Encounters.
When George is hanging outside the helicopter, above the water surface, he should be screaming in pain since the rotor-blades would whip up a pretty dense cloud of seawater, thus he would be injured since his race is extremely sensitive against seawater, as pointed out by Joshua Strader, and William Harcourt in the end scene, their bodies react to it as we would to sulfuric acid, as referenced in the movie.
After Francisco pulls Sykes out of the water he stops screaming and sits comfortably in the helicopter. Since his hand would still be wet, and his shirt and jacket soaking wet with salt water, he should still be screaming in agony.
While at the county coroner's, Sykes says he emptied a whole clip of bullets into one of the mini-mart killers. Pistols don't use clips, they use magazines. Any cop would know the difference and would not call a magazine a 'clip'.