The hospital was closed in 1931 yet much of it is lit with fluorescent tube lighting. Fluorescent tube lighting was not in commercial production until the late 1930's and not in widespread use until WWII.
(at around 36 mins) When Eddie and Sara walk into the Zoetrope room, the mic is visible at the top right of the screen, peeking out from behind the zoetrope tank. Eddie's flashlight shines right on it at one point.
(at around 1h 12 mins) At the beginning Sara introduces herself as Jennifer Jensen, but later on when she is looking for Melissa Marr just before shooting Price she is calling out to her saying, "It's Sara." But she only revealed that she is Sara while talking to herself.
Sara Wolfe's wandering through the basement is out of sequence. At one part she wanders into a darkened room filled with debris, but then in the close-up, there is a light through a door to her right as well as a clear path for her. In fact, the halls she wanders through keep changing from long shot to close-ups.
(at around 33 mins) When Pritchett, Sara and Eddie are first in the basement, and Sara give the torch to Pritchett. You see him raise his hands in the air, and neither of them shows any evidence of the cuts he sustained while breaking the glass in an earlier scene.
When Sara and Eddie are in the lobby en route to the attic (which is at the top of the tower, proven by the fact that when they escape out the window, that is where they end up), "the house" is right behind them. It is not plausible for them to be able to run all the way to the attic without being engulfed by the house.
(at around 30 mins) The characters claim they cannot tell if their pistols are really loaded because the magazines are "welded" into place. First, the pistols are all Sig Sauer P228 9mm which have plastic magazine wells which wouldn't be "welded." Second, like all semi automatic pistols, the shells can be manually unloaded via the slide, and can even be fully disassembled without any need to access the magazine well.
The movie is set in the present yet when the hospital was shut down in 1931, electroconvulsive therapy (electro-shock treatment) was not yet administered. It wouldn't be until 1937 which it was first used.
(at around 46 mins) When Melissa goes to the basement with her camera and her camera starts to show the ghosts performing an operation, it is an obvious recording as the camera begins to pan on the video before the actress moves the camera.
Some of the warnings in the basement are in very bad German - it seems somebody just used a dictionary and translated the English lines word-for-word. For example, one sign has the phrase "Steh zurück!" which means something like "Stay back!". A correct translation would be "Zurückbleiben" or in this context "Eintritt verboten" ("No admittance").
(at around 20 mins) When the camera tracks in on Schecter in the control room in the haunted house, there are two very conspicuously CG-added Blockbuster video boxes under some paper. They wobble as the camera moves closer to them.