The scruffy looking man who ultimately allows Nick Cassidy to prove his innocence is shown briefly in the scene when Mike Ackerman enters the police station and first learns there is a man on a ledge.
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.
When Joey finishes cutting into the wall with an electric concrete saw during the diamond heist, the blade is spinning in the opposite direction (away from him); Blades actually work by spinning toward the operator, not away.
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.
Sam Worthington helped kick start Man on a Ledge into production when he expressed early interest in the script. Worthington partially admits to being intrigued by the role because of his fear of heights, and the majority of the scenes on the ledge were set to be shot on the real ledge of the Roosevelt Hotel, over 200 feet above 45th Street in
midtown Manhattan.