Continuity mistake: Bryan is cornered in an Istanbul alley and engages in fierce hand-to-hand combat with Albanian gangsters. Bryan takes one of the gangsters hostage, holds a gun to the gangster's face and threatens to kill him. Another gangster doesn't even hesitate to shoot Bryan's hostage in the back multiple times, and the guy drops down dead at Bryan's feet. Bryan is frozen on the spot. Camera cuts to another Albanian gangster entering the alley, holding Lenore hostage. Camera cuts to close up of Bryan, who quickly calls his daughter Kim to warn her. Camera cuts back to a full view of the alley, and the dead guy at Bryan's feet has completely vanished.
Continuity mistake: During the end car chase when Brian's daughter is driving the taxi, she keeps crashing into things, yet in the shots of the taxi after there is not damage whatsoever.
Continuity mistake: When Bryan and Kim are on the ferry in Istanbul, he is wearing a scarf. This scarf varies between being rumpled in some shots and smooth in others, depending on the camera angle. (00:20:25)
Factual error: Bryan tells Kim to go to the US Embassy if he doesn't return in 5 minutes, and enters "US Embassy" into the GPS. Later there is a chase scene that ends at a building with "United States Embassy" on the signage. This is impossible unless they drove about 6 hours to Ankara, the capital city. Istanbul has only a US Consulate (albeit a very impressive one).
Other mistake: Bryan's daughter Kim has an iPhone - when you see the phone she has no signal, but is able to make calls from the phone. This happens twice.
Continuity mistake: When Kim leaves the hotel pool to return to her room she leaves behind her iPad on the lounger. When the gang members come looking for her at the pool her iPad is not on the lounger anymore. (00:34:50)
Continuity mistake: In the scene where Kim Mills steals a Mercedes w124 taxi and drives her dad with it to the House where her Mum is being held hostage, you can see that it is actually 2 different w124 models that are being used. (though with similar number plates). Also in the subsequent chase scenes, the camera also alternates between the two taxis.
Continuity mistake: Kim is cornered by the bad guy on the rooftop. Her braid switches from being over her right and left shoulder throughout the scene. (00:56:00)
Factual error: Liam Neeson asks his daughter to set the grenade off and counts to 4 after that. He then calculates the approximate distance of the hotel from the place he was taken to, by multiplying the speed of sound (0.34 km/s) by the time taken for the sound to reach him (~4 seconds). Given those numbers, the distance between him and his daughter is about 1.36 km, whereas he calculates it to be 4.5 km. He also makes a minor slip up in using "circumference" instead of "diameter" when she draws the larger circle, but that's incidental to the real mistake here. (00:43:00 - 00:44:00)
Other mistake: When Bryan types "US Embassy" into the GPS, the letters that he types on the keypad don't match up with the letters that end up appearing on the screen.
Continuity mistake: Bryan shoots the black Mercedes and it flips. The windshield falls right off. Three seconds later (literally), the windshield is still intact. (01:03:15)
Factual error: In the end credits, when the list of songs appears, look at the credit for Alex Clare's song "Too Close". His name is misspelled as Alex Claire, a very noticeable typo. (01:30:40)
Other mistake: During the first chase scene in the movie about 10 seconds after the man on a moped is knocked over you can see through the car's back window that a woman is walking at the same speed as the speeding car.
Continuity mistake: When the man in the white shirt is shot in the back, he's shot once, but there's two bullet holes.
Continuity mistake: Lenore's neck was cut, she was hung upside down and blood was collecting in the shroud. She was rescued by Bryan. Later in the movie there's no blood, no cut, no stain.
Continuity mistake: When Bryan is invited inside for a drink, his ex-wife takes a bottle of wine to the table in the kitchen. The wine glasses then are magically filled. (00:06:20)
Continuity mistake: When Kim is being chased by the bad guys on the rooftop the sun changes between shots.
Answer: I'd say there is no reason other than because it's a movie. Logic and reality are often supplanted in favor of more dramatic and exciting action scenes.