What's the flaw in the P != NP proof in the article "The Computational Complexity of the Traveling Salesman Problem"
Yes, you are right: there are plenty of other possible algorithms the author ignores. Briefly, the author claims that the $\Theta^*(2^n)$ dynamic programming approach in the paper is nessecary to solve TSP. However, he completely ignores any sort of structure that may or may not exist in TSP instances. 

So, we can look at special cases of TSP where we do know that we have special structure to see their argument is insufficient. For a simple example, consider the graph class where there is exactly one tour with cost $X$ and all edges not part of this tour have cost $&gt;X$. Clearly, we can find a tour in $O(|E|)$ by selecting all edges with cost $\le X$. Note that if the argument of this paper would apply to the general case, it would also apply to this one, so this is a contradiction with his argument. Clearly, even if the claim of the author is correct, he has not proven it.