Revealing mistake: When the plane goes through the smoke at the start, the smoke doesn't react in any way - it keeps rising. Surely the wind from the plane would make the smoke drift a different way. (00:12:25)
Revealing mistake: When Niles York first appears on camera beside the plane bearing his name, most won't notice, but you can see the pilot's hatch open, revealing that it is not a passenger jet, but a fighter plane. You can also see the air intakes on the wing, further evidence that this is not a passenger or private jet. (00:02:11 - 00:22:18)
Revealing mistake: When Luke is signing the receipt for his new clothes, the amount on the CC receipt is less than $10.00. (00:40:16)
Revealing mistake: When FDR jumps in the Beetle to help Lauren you can see it's a stunt making the jump - his hair is darker.
Revealing mistake: The SEALs assaulting Bin Laden's compound are using infrared lasers on their rifles, which can only be seen under night vision. The lasers being AN/PEQ-15s which the SEALs have attached to the top of their rifles. However, most if not all of the rifles have the laser beam coming from the bottom left of the hand guard, not from the top mounted laser unit. It's possible the/PEQ-15s were faux units and different lasers mounted to the rifles were used to give the effect.
Revealing mistake: After the officer collides with the taxi door, Wilee tries to think which route to take. The second one he thinks up is him ending up hitting a jogger and the jogger getting run over by a van. It's noticeable they used a dummy. Notice how the body flips over, completely unrealistically. (00:18:20)
Revealing mistake: In the car chase, the stunt ramps on the ground so that both cars can easily race over the curbs instead of destroying their wheels. (01:20:20)