Other mistake: A police helicopter nearly crashes and has to veer away because of the superheated air around the building when only a few floors are on fire, but Will Sawyer and everyone else can function normally when half the building is ablaze. In fact, everyone barely breaks a sweat despite being surrounded by flames.
Other mistake: Many of the scenes displayed on the monitors in the building and the local news footage of Will climbing the crane, swinging on the building ledge etc are depicted from a nice horizontal angle. There are no camera crews on the crane and there is no building nearby with such clear views. Nor is a news helicopter hovering filming the events yet hundreds of people gather to watch a huge screen as events unfold.
Other mistake: In the final fight scene, Will tells Bathos he is right behind him. Really? How? Bathos was facing a rather large hole in the floor he'd threatened to throw Will's daughter into just moments before.