Is the hotelling model wrong

Answer 1

There are two ways a model can be wrong. The first is if the author makes a mistake in solving it and deduces incorrect implications. In this sense the original Hotelling model was wrong, because Hotelling deduces a "principle of minimum differentiation" from it. In the 1970's using game theory economists proved that with simple linear costs, there is no pure Nash equilibrium. Furthermore, with quadratic transportation costs, firms instead differentiate as much as they can in order to weaken price competition.

The second way in which a model can be wrong is if it fails to reflect reality. Since there is no clear prediction coming out of the literature, it is hard to assess in this case (a problem with economics in general!).