(at around 25 mins) Near the beginning, Ben puts his left hand on the mirror. Suddenly, a large bloody gash is across his palm. When gets up, the blood and slash is gone. He catches on imaginary fire, it goes out, and his hand is still okay. When he gets home, his hand is bloody and cut again.
(at around 26 mins) Ben dusts himself down after the fire scene, and rubs his shirt down to make sure he isn't burned. If he was rubbing a clean white shirt with a bleeding hand that wasn't bandaged yet, he should get blood all over his shirt, but he doesn't.
In early scenes, when Ben is walking through the Mayflower, his jacket alternates between zipped and unzipped.
(at around 1h 8 mins) After Ben gets Anna's file he sits down to review it. At this time his hand is bandaged from the cut. When he sits down and proceeds to review there is no bandage. In the next scene the bandage is back.
At around 59 minutes when Ben is painting the mirror, the amount of paint changes between shots.
(at around 40 mins) Gary Lewis' driver's license is a laminated card. New York driver's licenses are pre-printed plastic cards, not laminated.
Ben returns to deal with the large mirror and fires a volley at the mirror from what looks like a Glock pistol. After the second volley, the pistol is empty. But, there are clicking sounds. A Glock, as with most semiauto pistols, wouldn't click after the last round in a magazine is fired. The slide would be locked back and the firing mechanism would be inoperable. The camera then shows a front shot of the pistol with the slide forward. You can see the breech end of the barrel in place in the ejection port. In the next scene, the slide on Ben's pistol is locked to the rear.
(at around 37 mins) When Ben is looking at the newspaper clippings on the Mayflower fire, a close-up of one clipping reveals it to be the same paragraph repeated over and over.
In 1952, they usually use typewriter, but Anna's hospital file uses computer fonts.
In the beginning of the movie, it was clearly stated that the burned-out store had no electricity. However when Ben Carson is in the basement breaking a hole in the wall, the florescent ceiling lights are on. There is also a close-up shot of an incandescent bulb flickering on and off.
(around 21:19) Afer catching fire in front of the mirror, when Ben puts his vest back on, seen from the back, behind the table under which his wallet is yet to be revealed, the mic can be seen on the right of the screen, slowly moving away.