Continuity mistake: When Pierce first begins to interrogate Caliban in the safe house in Mexico, a large portion of Caliban's albino makeup is smudged below his nose, revealing the actor's natural skin in his first close-up of the scene; after switching to a close-up of Pierce, then back to Caliban, the smudge has been fixed.
Factual error: After the Oklahoma City casino incident, it shows a brief scene where Pierce picks up Dr. Rice. The sign in the background says "Ada 15, Oklahoma City 90" on Highway 81. That highway in Oklahoma is, in fact, a real road but it is no where near Ada. The closest area that is 90 miles from OKC would be around Duncan, which is well over 50 miles from Ada.
Factual error: Logan and Laura emerge from an urgent-care clinic in a small town, presumably somewhere in the Great Plains or eastern Rockies. Shortly after they emerge from this clinic, a Louisiana state highway sign is visible in the background. As the scene ends, the camera pulls back to show mountains in the background, indicating that they aren't in Louisiana.
Plot hole: In the hotel attack scene, the bad guys were paralysed when Charles went into a seizure. Logan came in and drove his claws into several men's head. These men died and their brain function should have stopped and no longer affected by Charles. They should have fallen over, but they remained standing until Charles had his injection.