Continuity mistake: The car's inspection certificate is dated 07 2006, at the end of the movie when they drive off it's 08 2006. (00:06:28 - 01:57:57)
Continuity mistake: During Claire's post mortem, Doug takes a picture of her face. Her head was tilted towards the camera as were her eyes. When the picture comes out, it shows that she was faced away from the camera. (00:18:20)
Continuity mistake: When Clair is on the post mortem table being examined, look at her eyes. When her head is turned to the right her eyes are as well but when they turn her head to the left her eyes are left as well. Another scene shows her eyes appearing to be looking straight up. Unless her eyes were manually moved they wouldn't change positions after death. (00:18:20)
Audio problem: When Doug is staring at the terrorist and says, "I can see him, he's right in front of me", you'll notice that his mouth moves a little before words are actually said. This is because he first says "Jesus", but they took it out because the character playing the terrorist is Jim Caviziel, who played Jesus in Passion of the Christ. The filmmakers did not want to get a laugh out of that line which it inevitably did in test screenings. (01:06:10)
Continuity mistake: The rig Carlin is holding repeatedly switches between his left and right hand. (01:06:25 - 01:07:25)
Revealing mistake: When the truck leaps off the ferry, the underside is seen, exposing the still-flaming 'roll cannon' opening in the rear floorboard. This cannon is what caused the rear of the truck to rise, sending the truck flipping through the air. (01:52:30)
Continuity mistake: When the red Ford Bronco is driven off the ferry (ignoring all the impossible factors required for it to successfully do so), it flips through the air and contacts the water going backwards, its right/rear tail light entering the water first. The closer next shot shows the truck sink somewhat as it continues to flip backward, onto its roof. The very next shot shows the interior of the truck as it enters the water right-side up and going forward as water rushes in. Denzel lurches forward and down, driving his face into the water that is about waist level. The next exterior shot is underwater as the truck now lands in the water, nose first and right-side up. It then begins the expected slow dive, nose-first. (01:52:30)
Continuity mistake: When Denzel Washington is taking off his clothes to be sent back in time. We see him take off his blue shirt. The shot then changes to look at the other guy and we see him take off his shirt again.
Factual error: When the Bronco is underwater at the end of the movie, Claire's hands are tied to the steering wheel. Doug rips the steering wheel off. Anyone who has worked on cars knows you need a puller to get a steering wheel off, you can't just rip it by hand.
Factual error: In the Hummer scene, the signs that read "I-310 South, Bayou Bouef" and "U.S. 90 East, Bayou Bouef" in reality read "I-10 West, Baton Rouge" and "U.S. 90 East, Claiborne Ave".
Continuity mistake: When Carlin goes to the dock he gets out of the Hummer carrying a gun. The gun changes hands between shots as he is walking.
Continuity mistake: When Denzel makes a u-turn and a red BMW crashes, the front gets smashed, but a frame later, from a wide angle it's perfect.
Continuity mistake: In the scene where Doug and the terrorist are talking about 'destiny', the terrorist has a tiny bit of his cigarette left. But when the camera quickly shows a shot of Doug's face and then comes back to the terrorist, his hands are almost in exactly the same place, but the cigarette is gone.
Continuity mistake: In the beginning, the Pepsi can moves around between shots.
Deliberate mistake: After Doug finds where Minuti was killed and set on fire, he walks over to a dock where he sees Minuti's arm being eaten by alligators. Minuti had been dumped in the water 4 days prior, yet his hand is perfectly intact with no signs of burning, bite marks or weather/water damage of any kind.
Continuity mistake: When Denzel first leaves in the hummer he is on the Westbank heading toward the CCC Bridge to the Eastbank (downtown New Orleans). Once he makes it to the bridge, he's suddenly headed back to the Westbank (away from downtown) but on the Eastbank bound span (bridges are one-way), only to exit the freeway and suddenly appear on the Eastbank and cause the accident with the 18-wheeler.
Continuity mistake: When the cop woman drags a timeline, the drawing keeps changing all the time. Watch the shape of the "X" for example.
Factual error: When Denzel Washington wakes up in the hospital he unplugs the cables attached to the heart monitor. By doing this he shuts down the monitor. Actually those monitors go into yellow alert by disconnecting the heartbeat sensors. They can be configured to do nothing at all by disconnecting but they will never shutdown this way.
Continuity mistake: While watching Claire in the shower she turns her head to her right. A frame later, from a new angle, she repeats the movement.
Deliberate mistake: When Doug is in the Hummer chasing the terrorist, you are given a first person perspective of Doug wearing the goggle rig. A split screen shows one view (his right eye) of present day, and the other, 4 days in the past (his left eye). If you look closely, the present day shot will pan right and the other shot will pan left, yet they should be looking in the same direction at all times.
Answer: Not a definitive answer, just an "allowable" excuse for this... The time surveillance team is testing their equipment and rigs and it's merely a coincidence that they happened to be in this area at this time.