In the flashback at the beginning (at Sing Sing Correctional Facility, a month earlier), while talking with the psychiatrist you can see that Nick has plaster on his arm, due to the fight we saw before. In the next scene he gets a visit from Mike, but then his arm is no longer plastered.
The building used in the outside shots clearly was the Roosevelt Hotel, but the Roosevelt (and all outside shots of the building in the movie verify this) has only 18 floors, and the movie premise is a hotel of at least 24 floors.
After Joey opens the panel beside the vault door, Angie looks into it and we see the vent beyond goes on for a fair distance. However, later in the movie, we see into the vault itself and it's evident the layout of the vault and corridor couldn't possibly accommodate a vent of the length shown.
When Joey stops the fan and bends the blade down so that he and Angie can get to the elevator shaft, the bent blade is pointing up at a 45 degree angle. As Joey and Angie are rigging their ropes to drop down the shaft, the bent blade changes from 45 degrees up to 45 degrees down, and back a few times.
On the rooftop of Englander's building both Joey and Angie are seen reaching the bottom of a ladder before Joey speaks to Nick from his phone. In the next shot the camera is positioned up with Nick and we see Joey at the bottom of the ladder but Angie only half way down.
When Lydia Mercer is talking to Ackerman in the hotel room, she's holding an orange coffeecup. In some shots you see the front side of that cup with a logo. In other shots you see the back with a barcode.
Nick is very careful to remove his fingerprints from everything he touched in the room prior to going out on the ledge. However he opened the window to access the ledge and did not clean his fingerprints from the window frame. That would be an obvious place for the forensics team to look but they stated that they could not find any prints in the room.
Before Nick goes out to the roof he uses the bathroom sink to wash his face leaving his fingerprints behind. He is never shown wiping them off and the forensic team is said to have wiped the hotel room without coming up with any prints.