Many of the soldiers in the film are wearing the Army Combat Uniform (the digital gray fatigues) turtleneck style. The ACU is only worn with the collar up under body armor, to keep the armor's ballistic throat guard from chafing a soldier's neck. When worn by itself, the ACU's collar is folded down, resembling an open collar shirt with lapels.
After Greer crashes his own car into the boutique and escapes down an alley. He see's a man in a gray suit get out of his own car and walk to the front of the car. Greer then jumps in the drivers seat and as he drives off, you see the original driver, but now he is wearing a black suit and is now running back from behind the car, where previously he was in front of it, shouting at Greer.
In the elevator going to see Dr. Canter, Greer is standing next to the bodyguard and glances over to see a gun under the bodyguard's jacket. In the following shot, no one has moved and as they begin to exit the elevator, Greer is now behind the bodyguard and would not have been able to see the gun from there.
When Tom Greer is talking to Lionel Canter's young man surrogate in the back of the limo, the surrogate's hair changes dramatically within seconds. Tom Greer looks away for a second and when he looks back the surrogate's hair changes from in place and shorter to longer, shaggy and in his eyes.
The car which Peters crashed and is used by Greer to chase her, has no visible damage in 2 of the following scenes. One of these scenes is after Greer crashes into the store. The FBI agent opens the driver's door and we briefly see some cracks in the passenger window, no other damage to that door.
In the ending scene when Bruce Willis' character is holding his wife in his arms, the closeup scene shows his right arm in her hair and his other arm around her back. In the very next shot as the camera backs up, the hands are switched.
When Bruce Willis and Radha Mitchell's characters look at the destroyed surrogates, the cop tells them they should go talk to the owners. The next shot is an over head of the Zakim Bridge, but the angle shows the TD Bank Garden on the right side implying they are headed south on the bridge. The Zakim is located north of Fort Point Channel, thus, you wouldn't ever travel southbound if you're leaving Fort Point Channel. The Channel is a body of water that borders South Boston.
When the FBI agents investigate the damaged army surrogates, they visit with Colonel Brendon, who is seen wearing a Ranger tab on the right shoulder of his Class A uniform. Special skill qualification tabs are worn on the left shoulder only, not the right.
When Agent Greer meets Col. Brendon in his office, Col. Brendon is wearing the U.S. Army "Class B" uniform (shirt & tie, without the Class A jacket). His Class B shirt should have, as a minimum, a name tag and rank insignia shoulder boards. While U.S. Army uniform regulations could change in the future, it's unlikely that they would change to where you would be unable to identify the soldier's name and rank, especially since his ACU fatigues and Class A uniform are identical to 2009-era U.S. Army uniforms.
When a young man is killed at UC San Diego, his body is loaded into an ambulance. By California state law, it is Coroner's Office vehicles, not ambulances, who carry corpses. However, the movie is set in the future when that may have changed.
At the end of the film, mild damage from cars on some (not overly busy) inner city streets is shown, and voice-over newscasters are heard saying that there were zero human casualties. One might think that surrogates operating airplanes, when disconnected, would crash and kill human passengers. Still, there are two reasons this might not be so: first, human populations were seen as subsisting without technology, driving a horse-cart for example. No airplanes are seen in the film, likely because, as Maggie Grier explains, a vacation means operating a long-distance surrogate, not flying (one's surrogate) to a remote location.
When Bobby shows Peters how he can "Buffer" people from their surrogates, the robots freeze in place. When Greer "Buffers" everyone to prevent them from dying from the virus, the robots continue to move. They should have stopped as soon as the buffer took place, isolating people from machines.
When Peters is being chased by the car and jumps off the phone booth to the building and back to the street, the actress is wearing high-heeled pumps, but the stunt-woman is obviously wearing athletic flats. This is seen again when she jumps onto the bus.
The goof item below may give away important plot points.
When Greer goes to confront the real Lionel Canter he is stopped by one of the bodyguards in the lobby. As the bodyguard twists Greer's arm and Greer pulls his revolver to shoot him in the stomach you can clearly see the gun firing without Greer pulling the trigger, as indicated by the hammer of the revolver staying motionless.