Irwin Allen originally wanted Steve McQueen to play the part of building architect Doug Roberts. McQueen however, fought for and got the role of fire chief O'Halloran. The role of Doug Roberts went to Paul Newman.
Steve McQueen was married to actress Ali MacGraw at the time. Right before filming the dangerous and climactic scene in the Promenade Room, he told everyone, "If anything happens to me, Ali gets my pickup truck."
Lifting the brakes on the scenic elevator would not involve cutting wires and shimming relays (unless there was still power, in which case the brakes wouldn't need to be lifted. Manually lifting the brakes would require large wrenches on the elevator machine itself, and could not be done in 30 seconds.
When the electrical junction box explodes open in the storage closet on the 81st floor, a fairly thick wire flops down and sparks. The thick wires in such a box are made out of bundles of copper wire, too stiff to flop down as shown in the movie.
Dan and Lorrie and having an illicit affair. They are both eager to keep this from being discovered as evidenced by some of their dialog during their tryst. When the couple discover the fire and Dan makes his fake phone call, Lorrie has no reason to doubt him. Yet though her clothes are draped on a chair in the same room, she makes no attempt to get dressed. Instead, she remains wearing only Dan's dress shirt and a pair of control top pantyhose. She apparently means to greet the supposed rescuing fireman dressed this way-- and be escorted down to the lobby barefoot in pantyhose with her boss at her side. Given the situation and circumstances, Lorrie's first action after Dan reassured her that "help was on the way" should have been to put her clothes back on.