When John Cena is dropping off his daughter at school, he first says "don't forget your book bag" and then there's a scene cut and he immediately says "don't forget your backpack".
A tattoo on Claire Wellington's side is supposed to be the Latin for she flies with her own wings (the state motto of Oregon). However the tattoo is misspelled; the word propriis is missing the second letter r. There are a few places on the Internet the same mistake can be found. Given one meaning of the motto is that she doesn't necessarily follow convention, perhaps the misspelling was originally a joke.
When shooting the Barrett, Mason leaves virtually zero eye relief between his face and the scope. The recoil and subsequent scope to the eye would cause him some damage.
When battling with the helicopter, when Mason mounts the rifle on the log, and after shooting the chopper, the muzzle is clearly blocked with a cross section, showing it to be prop/stunt weapon.
During the firefight at the presidential palace office, you'll notice at some scenes that the guards gun were firing without the men pulling the triggers.
In the presidential palace firefight, as Claire huddles up behind the presidential desk, her lav mic is visible taped to her lower back.
When Mason meets the mercenaries to do the exchange, Cena's mark is visible on the ground between his feet.
Each time Mason dispatches one of the heavily armed mercenaries chasing them, he never takes their weapons for defense against those still hunting him, which is totally out of character for an ex-special forces operative.