The building is shown to have fire escapes. That would have been a far better option than the elevator, which likely would have gotten everyone killed.
When the fire captain gets into his car to go to a fire, if you look closely you can see on his door the seal for the city of Los Angeles. The show was set in New York.
Photographer "Claire Harrison" is not holding the camera properly. Her finger is nowhere near the shutter button.
When McCloud is forced to jump off from the burning building, his hat stays on all the way down and is still on after he lands.