He could hack the problem like this: instead of figuring out which type of dancing is impressive directly, just watch reactions. People react to what they think is good dancing, so by watching people he can learn what's considered good dancing.
In the context of Adams' mind experiment there's a problem with this approach: the aliens need to now both there is a goal to dancing or conversing well, and what that goal is. (Which is confounded a bit by there being multiple goals for these activities, and not everybody's going for the same ones in any given context. Two people who just met will want a different thing from conversation than two friends shooting the shit.)
However, Adams' rhetorical questions (though not, I think, his mind experiment itself) have a flaw: people with Asberger's syndrome generally know what the goal of those activities is (or at least, what they want out of it), but are unable to judge whether they're actually achieving those goals (since they have a hard time gauging other peoples reactions as you suggest).
This fits with the mind experiment though. Suppose the aliens figure out that conversation and dancing have goals - even what those goals are. The alien still can't tell who the good conversationalists or dancers are without understanding things like human body language, vocal inflection, or subtle word choice - which is nearly the same set of problems people with Asberger's have.
The whole thought experiment is a bit weird, because the range of dancing skills on display in the typical nightclub in all the parts of the world I've been to recently is really not that large.
I think it's much tricker than you said. Those are just a variety of small details, and there are many more in the same general category. But that doesn't stop it from working. It's very noisy data whatever you do. The difficulty may approach that of learning English while you're there. That could take a decade, who knows. Children learn English faster than that, but we do lots of things to help them, but OTOH the alien is super smart and has computers to analyze patterns in the language.
(Of course if the alien does pick up English, these context problems become pretty small.)
I took the original question to be about the fact that what constitutes a good dance move is arbitrary. That's a fundamental problem. How do you figure out something that's just an arbitrary convention? Well, the solution is to look at the people who decide it.
How people react to stuff, like what they say, is not arbitrary. There's a method to it that you can figure out, unlike dancing which arguably doesn't have a method (I'm not taking sides on that, I just interpreted the problem to be to assume dancing hasn't got a logical method to it).