Continuity mistake: When Memphis is taken hostage his telephone falls on the middle of the sidewalk. In the next shot it lies on the edge.
Factual error: Right after the 'trap' for Swagger, two soldiers enter the house with Swagger waiting for them on the inside. Swagger shoots the first one twice, but after wrestling with the 2nd one for a bit, Swagger shoots through the safety helmet to kill the 2nd soldier. This would be impossible since these helmets are made to withstand much tougher weapons that a 9mm Beretta. What's even worse is that the blood comes out on the other side, meaning that the bullet pierced the helmet twice.
Factual error: When FBI agent Memphis is reviewing the assassination on video, you can hear the shot first and then see the blood spray of the bullet impact on the Archbishop. This defies physics as bullets travel faster than the speed of sound. Given the distance the sniper shot from, the sound of the shot would be be heard a second or 2 after the impact.
Other mistake: In a whole lot of scenes, Bob closes both his eyes when he fires his sniper rifle. This is a common and natural reaction when an inexperienced shooter fires a gun. An experienced hunter or marksman would never do that, and especially not a military sniper.
Revealing mistake: When Gunny snipers the shotgun (and hand) off the bad guy in the snow covered mountains, his rifle is right-handed bolt, and he shoots right-handed except for the mountain scenes. He closes his right eye before he shoots, and it even shows a close-up of his left finger on the trigger, obviously a flipped shot.