When Kim sets off the first grenade, Bryan counts nearly 4 seconds and calculates that it was 4.5km away. The speed of sound is approx 0.340km/s so the explosion was just over 1km away. The sound would have taken roughly 13 seconds to travel 4.5km.
When Kim is making circles on the map, she compares the shoelace to the map's scale as a reference, but doesn't hold the lace flat against the map when drawing the circles; instead, the lace acts as the hypotenuse of a right triangle, with the pen and map as the other two sides. Any circles drawn in this manner would be smaller than intended.
When Bryan asks Kim to draw circle on Map. For the first circle, he tells Kim to "make DIAMETER of 3 Kilometers". Then later, for the second circle he tells Kim to draw a circle with "CIRCUMFERENCE at 4.5 Kilometers". Kim draws circles considering both the distances (Diameter and Circumference) as Radius.
When Bryan sets the 5 minute timer, the clock at the top of the phone's screen reads 16:51, when Kim next looks at the timer it reads 3 minutes 24 to go, however the clock now reads 16:42 (9 minutes before the timer was set), the subsequent shots of the timer are consistent with this.
After Bryan notices he is being tailed with Lenore and takes the BMW, he winds up driving through a food stand. Throughout the scene, the car constantly changes between being dirty and covered in food and perfectly clean.
When Kim is being chased on the rooftops of Istanbul, the distance between her and the man chasing her changes drastically between shots, switching from about 10 feet to 30 feet and then coming back to less than 10 feet.
When Mills is at the hotel and receives an envelope containing money, he tucks it in his jacket pocket. The jacket it clearly buttoned up and he doesn't unbutton it, however in the next scene when he pulls out his phone, it is unbuttoned.
Kim is shown Skyping her boyfriend at the pool using an iPad. When she the call from her dad, she runs from the pool, taking only her cell phone and leaving the iPad behind. Later when the villains come to the pool with the intention to abduct Kim, they search all around the pool and the iPad is nowhere to be found.
When Lenore and Bryan sit down to have a glass of wine Lenore brings two empty glasses and a bottle of wine to the table but she never pours any wine from the bottle, yet when they bring the glasses to their mouths they suddenly contain wine.
There is no common border between Albania and Turkey. The Albanians would have to go through Greece, or Serbia, or Macedonia. There are mountain passes, but certainly the border crossing points cannot be that primitive.
The women in the film are all wearing the black hi-jab which covers all the body even the face, which is rarely seen in Turkey. There are no ladies appearing in the film with modern clothes or without hi-jabs.
The soldiers guarding the U.S. embassy in this Middle Eastern country would of course assume a car barreling down on them must be a terrorist attack and keep firing their assault rifles and the heavy machine gun. There is no chance to survive this kid of approach in a simple car with no armor.
When Kim waits Bryan in the stolen Mercedes taxi, a navigator front screen is barely shown. On the screen it is written in Turkish 'GPS KAPALI' means that GPS is turned down. Under this condition it is impossible for navigator to find the address of US Embassy.
So Bryan has only two people on his secret emergency phone? One of them his daughter? It obviously has a touchscreen and at least three contact storage 'slots'. No reason it should not hold a dozen contacts. A well-prepared ex-spook would at least have the U.S. embassy on speed dial, possibly even the police or the local CIA station.
Ever seen one of these funny Internet videos where a new military recruit practices throwing a hand grenade, fumbles it and is pulled into the trench by his instructor in the very nick of time? No way this obsessive father would let his untrained daughter anywhere near a grenade.
Either Bryan uses super secure high tech crypto cell phone technology so his emergency mini phone cannot be located even by the NSA. Why would he do that? OR Bryan's first call to his daughter from that phone could have been traced by U.S. intelligence assets like any other cell phone, in which case he should have insisted his daughter go to the embassy and have the authorities get the caller ID from her cell phone provider.
While Bryan Mills and Kim are being chased by Albanians, Mr. Mills gives Kim directions to the U.S. Embassy using a navigator. But the device screen reads "GPS Kapali" which is "GPS Deactivated" for Turkish. Besides, the device screen shows them driving on a coast highway; however, the chase takes place in narrow streets of suburbs then.
The goof items below may give away important plot points.
During the chase with the stolen cab, it crashes into a number of other vehicles, front and back, and through a number of obstacles, yet when it finally stops in the American Embassy, it has remarkably little damage.
After crashing into the US Embassy, Bryan calls his former colleague in Los Angeles, who is playing golf. With an 11 hour time difference between Turkey and the west coast of the USA, it would be highly unlikely that both characters could be in daylight at the same time.
Security at the U.S. Consulate in Istanbul is provided by local guards, not the U.S. army. There are always jersey barriers or other reinforced structures to prevent someone from just crashing into the compound as was shown in the movie.