I think there are a few ways people determine "coolness"
Firstly, how interesting the moves are affect the rating, usually with the more unusual moves getting higher ratings. However, some people might try for a while with harder problems and get frustrated with it, thus giving it a lower rating.
That leads to another factor of coolness: frustration. People get frustrated with either problems that have too many variations that can't be all thought through or they just try for a while and can't think of an answer. Obviously, more frustrating problems receive lower scores.
Which leads to another factor: amount of variations and length
I think people normally prefer problems without too many variations, especially if, as said before, the valid ones are not accounted for and fully explained as wrong. Also, though, there is a point to how few variations you could have. This comes down to personal preference. The length of the problem is also part of it; usually, the ones that go on longer than the person thought it would are more interesting, and would probably receive a higher score. To some, though, long problems are exhausting and monotonous and would receive a low score.
Coolness really comes down to just everyone's preference and how much they like the problem. That really is the definition of "cool" too (besides meaning slightly cold). The rating system, besides the fact that it lets people rate and re-rate, is not flawed at all and lets people know how likely it is that they would like the problem.
{Posted by ketran0}