At LAX, Brian discovers the map and drops his daughter off on the arrival level, even though her flight is departing for Paris. You can see they are on the lower level, which is the arrival level at LAX.
When the girls are in the apartment in France, they turn the music up loud so they do not hear Kim's mobile phone ring. When the camera pans over to her handbag, the phone is ringing, but "Silent" mode is selected.
When Kim makes a phone call just before getting kidnapped, she describes the man as having a beard. When Bryan hears this recording on the plane, it's changed to mustache, and again in a later scene when Bryan is listening to the recording it's beard.
When Amanda was taking a photo, the camera phone was held in the landscape position, but when Peter was taking the photo for them, he held it in the portrait position. Later, when Bryan was reviewing the photos, all the photos were in the landscape position, including the one supposedly taken by Peter.
When Bryan listens to the recording of his daughter on the airplane, the recording starts when his daughter says "They've got her", which would have been when his daughter was in the bathroom. Bryan originally started the recording after his daughter was under the bed in the bedroom, so the recording wouldn't include that part. It also would've recorded Bryan's voice, which was not on the recording.
After Bryan Mills saves the girl from the construction area brothel, he drives away in a white SUV. The pursuing bad guys shoot out the back window. The same window is intact in several following scenes.
When Bryan is in the apartment of his friend the corrupt French policeman, they use the policeman's computer to check on the identity of St-Clair, the man who is auctioning Brian's daughter. The computer is shown as having a QWERTY keyboard which is not the type used in France. It should be an AZERTY layout which is the type used in France.
When Bryan Mills tries to enter the apartment in Paris where his daughter was kidnapped, he uses a brown paper bag with groceries to appear a resident. These paper bags are typically American and not to be found in supermarkets in Paris, or most other parts of Europe.
Some men at the construction site wear hard hats that are not available or permitted in France. But seeing how the site is also the place for some VERY illegal trafficking-, narcotics- and prostitution crimes, it is not unlikely the men working there were also criminals and/or illegal immigrant workers who had brought their own equipment.
Bryan's only lead on Staint-Clair is the address 26 St Louis en l'Ile, Paris, obtained when Jean-Claude searches for him in the database. However, the mansion where the party is hosted is not the same building located at that address, as can be confirmed by a Google Maps Street-level search.
Bryan's diversion with the small walkie to avoid being caught when the French agents detect his cell phone location cannot work in the way depicted. First off, walkies usually are PTT, so either you can listen or you can talk, but to change from one mode to the other, you need to push a button.
Even if these walkies were to transmit and receive at the same time without hitting a PTT button though, Bryan would have to either dial or pick up the phone before he could start moving to his alternate location. That alternate on the other roof was too far for him to have reached it in the few seconds that pass between the start of the conversation and the first shot of static Bryan with his binoculars. But even if they had shown him on the move rather than observing, the French agents would have known he needed to stay in range of the low-power Walkie for the trick to work, so he could not be more than a few dozen yards away.
When Bryan listens to the mobile phone and the call ends, the audio sounds like a home phone cutting off, not a mobile. It's actually the sound of the phone being smashed. Later, the phone is discovered smashed.
When Bryan attacks the construction site, no one knows what he looks like, yet they know who to shoot. They could know each other by sight. Bryan, who is several inches taller, with much fairer skin and hair, stands out as someone who shouldn't be there.
Bryan is told that the kidnappers do business in "Yugoslavia," but no political entity has used that name since 2003. However, many people are not up on smaller countries' name changes, and use older names for countries out of habit. Since this movie was made only five years after then, it's a reasonable mistake to be made by someone not up on all international news.
At the end of the phone call during the kidnapping, the kidnapper (Marko) says, "Good-luck." Bryan is holding his cell phone to his ear with no wires attached, but later while on the plane, Bryan listens to the "Good-Luck" over and over. That would not have been possible since his cell phone was not attached to the recorder when that was said.
When Bryan is chasing the sheik's barge along the Seine in his car, he appears to be traveling at high rate of speed alongside the barge. The barge would likely be traveling around 5 knots, about the speed of a light jog. The speed limit for boats on the Seine is 15 knots, (about 17 mph), so even if the boat could somehow travel at the maximum speed for the river, (which would be impossible for a boat like that), it would still be at a crawl for a car.
Bryan tells Jean-Claude that he has 96 hours to find his daughter, which was 16 hours ago, during a scene in full daylight. The kidnapping was shown to have taken place around 11 AM in Paris, 2:00 AM in Los Angeles; 16 hours later would have been 3 AM.
When Bryan finally finds his daughter being auctioned off, she is heavily sedated; her facial features are relaxed and her orientation is off. When she is saved minutes later, she is completely aware of what is going on and the drugs have worn off, unlike the girl Bryan rescued before. Saint Clair didn't use the same drugs Marko used to sedate his girls. His clients didn't want their girls sweaty and unresponsive, like the girls in the trailer. It's entirely possible that Kim recovered to the point of recognizing her father by the time she was rescued.
Early in the movie, Sheerah's vocal coach, Gio, is presumably the black man rehearsing with her before she goes onstage at a concert. At the end of movie, given the implied context of the visit to see Sheerah, the person at the piano is not the same man. He may be an accompanist. Since the whole house isn't visible from the front door, Gio could easily be somewhere off-camera.
When Bryan leaves Marko with electricity running through him, Marko screams with his mouth open. The electricity would force his mouth to close. This is why Bryan puts the handkerchief in his mouth earlier, so that he did not bite his tongue or push his teeth, allowing him to answer questions.
When Bryan chases Peter up the ramp, he turns into heavy traffic with squealing tires. After Peter dies, Brian walks on the highway near the cars. The highway is a virtual parking lot, with empty cars, no noise and no brake lights, as you would see in a traffic jam.