I disagree; Dispute the entire bill even though you are not trying to get out of paying what you really do owe them.

You will get a much faster response as they will fight to get what is due them (one night) and that will force them to prove that you were there nights two and three. The objective here is to get a timely response and start some sort of dialogue with the hotel.

At the point where the hotel challenges your dispute then all you are doing is contesting the disputed nights and will eventually pay off the first night.