Corrected entry: Hans and most of his men arrive on the 30th floor party and begin firing. Upon hearing the shots, McClane grabs his gun and is able to sneak into the nearest stairwell and climb up a few flights of stairs (he checks and passes the 31st floor, where a few more of Hans' men are spotted wheeling supplies) before finally arriving at the 32nd floor to begin seeking help. For essentially the remainder of the movie, McClane remains "above the danger zone", so to speak. However, it is fair to theorize that when McClane initially reached the stairwell undetected, he could have also descended to any number of other floors to then seek help. Even if many of the lower floors may not have been open (locked, not finished, etc.), McClane could have simply descended as far down as the main lobby (and out the front doors). Remember, Hans and his men were not aware of a straggler at first, and in theory all McClane would have had to do is descend the stairs to the main floor and get past the lone terrorist acting as the "security guard" at the desk.
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Correction: To what point though? That would work if McClane is trying to escape. But he's not. He's trying to stop the terrorist and talking to the police on the radio. His wife is in the building. He's not wanting to get out, he's wanting to save her and stop the terrorist.
Quantom X ★
That is correct, but you were thinking too far ahead. For the first few moments, John is simply trying to summon help (which is evidenced by him pulling the fire alarm and hoping that proper authorities arrive), and take care of it from there. He only started doing that after he found that he could not get past Hans and his men - because they were already aware of his existence. In one frame of thinking, it may have been easier to get the help needed for both his wife and everybody else if he just could escape the building all together, which he may have had a good chance of doing if he went down the stairs toward the first floor.
So the character made, in your opinion, a poor choice. This does not constitute a mistake.
It would have been a pretty pointless movie though wouldn't it?