During the shootout near the end Mills is holding a machine gun when the explosion throws him to the ground but when he gets up he is holding a pistol.
When Vox comes through the door of the prison Santana turns to look at him but in the next shot she is still looking at the glass booth.
When Christina is talking with the Lt. General at the National Gallery it is clear the medals on the Lt. General's uniform is wrong. The Good Conduct Medal, which is given to enlisted men, is in the topmost position on the rack of medals and the Army Commendation Medal is shown in the second medal, which would also be very unlikely.