Plot hole: In the original timeline in which the movie begins, Carlin is investigating Claire Kuchever's death including her missing fingers. In this same timeline we hear his co-worker tell him that his (Carlin's) fingerprints were all over Kuchever's home. We later find out that the killer cut her fingers off. However, the reason Carlin's prints are all over the home and the reason that certain items are set up in a certain way, was because Carlin was in the home with Kuchever after preventing her death and preventing her fingers from being cut off.
So the flaw is: if he kept her fingers from being cut off, he would have been in the home and would have left the prints but her corpse wouldn't be missing fingers (if she died at all). If he didn't prevent her death and dismemberment, he wouldn't have left his prints and certain items in her home. These scenarios could not both occur however.
Revealing: 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. Submitted by John W Rosa
Continuity: 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.
Deliberate "mistake": 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.
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.
Deliberate "mistake": In the scene where 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.
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: 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. Submitted by Sacha
Continuity: In the beginning, the Pepsi can moves around between shots. Submitted by Sacha
Continuity: When the cop woman drags a timeline, the drawing keeps changing all the time. Watch the shape of the "X" for example. Submitted by Sacha
Continuity: While watching Claire in the shower, the black woman turns her gead to her right. A frame later, from a new angle, she repeats the movement. Submitted by Sacha
Visible crew/equipment: When taking a shower, Claire is wearing underwear to stop her butt from being seen. Submitted by Sacha
Plot hole: The bad guy soaks the woman with fuel. The bad guy then shoots Denzel, and runs outside. He then fires at a propane tank that causes the entire building to explode. The fireball is enormous, and flaming debris is everywhere, including being inches from the woman. But she never ignites. Submitted by John W Rosa
Continuity: 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.
Plot hole: At the beginning (and the end of course) of the movie, Denzel's phone rings - the one on the Denzel in the body bag. First off, a cell phone that was submerged in water like that should not ring at all. Secondly, the phone the live Denzel has on him ring if someone calls that number in his reality

