The gun used by the bad guy on the boat clicks several times as he repeatedly pulls the trigger. This gun is a Glock, which requires movement of the slide for recocking. Hence, only one click would be possible.
When Angela watches the news about Jeff Gregg in her motel room, she is watching a Sharp brand television. When there is a close up of the TV screen it is a SONY, in the next wide shot the TV is a Sharp again.
At the park, the sound of Secretary Michael Bergstrom shooting himself spooks some nearby birds to the point that they take flight. However, the birds begin their panicked escape before the gunshot sound is heard.
When the paperwork for the temporary visa is initially revealed, it enumerates Ruth Marx's birthday as March 5, 1968. But when the police consult their database for Wants/Warrants on Ruth Marx, their system reports Ruth Marx's birthday as June 11, 1968.
When Angela gets off the elevator at Cathedral, we clearly see the number 20 posted on the elevator door frame, indicating that she is on the 20th floor. A few minutes later, it becomes clear that she is on the 5th floor, when Ruth calls for security after Angela copies the disk.
When Dr. Champion first meets with Angela in the hotel room, he tosses some folded clothes to her. In the shot where the clothes leave his hands, they are beginning to flip over forward, but when the camera switches to Angela catching them, they land perfectly upright.
When Angela knocks Devlin over the railing with the fire extinguisher, she lets go of the extinguisher as well. Yet the extinguisher never falls with Devlin, it is just shown in the next clip already on the floor.
When Angela is at the airport waiting to leave, it's heard on the speakers that everything has returned to normal and the planes are ready to be boarded. The military men seated behind Angela get up twice. Once before she gets up and again when she gets up herself.
When Angela runs the car of the FBI agent into the parked car Devlin is sitting in, Devlin's car should be visibly damaged on the passenger's front side. But in the following scenes it's completely intact so that even both headlights work.
When Angela was hiding in the center room of the carousel and Devlin was chasing her, she was looking out the slightly opened mirrored door. Devlin can be seen reflected in the mirror standing next to a fixed seat on the carousel and looking backward, against the rotation of the carousel. The next shot shows him walking amongst the carousel horses, then stopping next to the fixed seat, then stepping off and into the center.
At the Cathedral, after Angela tries to delete her profile at fake Angela's computer, she approaches the window to check out the fire engines outside. The opposite building bears the flag of USA. You can see this flag overhead the crowd of Cathedral employees at the next scene (the scene when the fake Angela asks the fireman about the smoke). This means that the Cathedral employees are just somewhere near the flag but at Angela's perspective, the crowd of Cathedral employees are nowhere near the flag.
In the first scene with Angela, when she hangs up the speaker phone, she hits the Handsfree/mute button. The light that comes on either mutes the call, or answers the phone - it does not release the call.
When the man is telling the fake Angela Bennett to get out of the building because of a fire, there is a shot to Angela hiding behind the wall, and in the background we see the fake Angela stand up. But when we see the fake Angela again, she is still sitting down.
After Angela has set off the fire alarm at Cathedral and made the others leave, she checks the computer. She hears the fire engines outside, and walks over to the window. As she walks, we can see the camera rig reflected in the cubicle wall glass.
During the opening sequence, when the Secretary is being driven in his car they are proceeding down Pennsylvania Avenue, but when the camera cuts to the view from the right side of the car there is a large expanse of water to the left. This would be impossible, as Pennsylvania Avenue is in the middle of downtown Washington DC.
Angela sleeps overnight in Alan's car, is woken in the morning by the security guard and she drives away with the Pacific ocean on her left. But as she drives northbound, the shadows indicate the sun, also on her left, is setting, so it must be late afternoon, not morning.
Right before discovering Bergstrom's mis-diagnosis of Aids, she connects to a system using the telnet command with an email address that was written on a card she had taken from Devlin's wallet. It is impossible to establish a connection using telnet with an email address. The only way to connect using telnet is with a FQDN (Fully Qualified Domain Name) or IP address (and/or a TCP port number). Once the telnet connection is established, you can however login to a system using an email address.
When Angela is driving in the BMW on the Highway with the police car behind her, the raindrops on the side window are going down on it vertically, but they should be blown a little backwards by the airstream. Also the raindrops on the windscreen of the police car should go upwards to the roof because of the airstream, but they just run down on it.
When searching for Praetorian, Angela searches for the owner of IP address: 24.75.345.200 This address would be impossible on the Internet because no subnet address can be greater than 255. This has been reported as a goof, but it was surely deliberate by the filmmakers. It would be very poor practice to show a genuine, usable IP address, because the present or future owner of that address would undoubtedly be subject to massive flooding, ranging from spam to actual malicious hacking attempts. This writer noted the same fact at "Swordfish" in the Trivia section, http://www.imdb.com/title/tt0244244/trivia.
When Angela Bennett gets her temporary visa using the name Ruth Marx, the lady shows her the form and asks her if that was the correct address, Angela nods and says it is but Ruth Marx is not her name. Presumably she didn't notice it, since her attention was drawn to the address portion.
When Dale is on approach to Burbank he says he is intercepting the approach course ILS runway 8. He then reports just passing the middle marker which is only 0.4 miles from the airport and way too late for him to be intercepting the final approach course. He reports at 1300 feet (he should be at 1000), but the altimeter shows 620 feet which is below the airport altitude of 775. Also, the GPS shows him still 35.4 miles away from the airport. (Additionally, the entire approach is conducted in visual conditions where he'd be able to see the approaching towers from a long distance away.)
The goof item below may give away important plot points.
Jeff Gregg's ID picture, presumably a big "reveal" moment, is shown several times during the "Praetorian login" jumble of images. As his is the only face shown during this, the careful viewer will have figured out long before that he is involved.