A fine description of the decision process for graduate admissions from the folks at orgtheory.net. Almost all of it carries over from sociology to economics, with the exception of the fact that in economics you basically must have a GRE math score over 750, if not over 780, or you are done.
I would reinforce two additional bits. First, most letters are completely uninformative. And the reason for that is not that the letter-writers would not like their letters to be informative, but rather because they have very little information about the student requesting the letter that is not obvious from their transcript. I wrote five or six such uninformative letters this year for students from my undergraduate regression class. What I can add to the transcript is (a) information about course content - which is relevant for places looking to hire regression runners, but not so relevant for graduate schools; (b) their relative rather than absolute performance in my class and (c) information about the overall level of grade inflation at Michigan as it relates to their transcript as a whole.
Second, at some point in the winnowing process it comes down to randomization and hunches. When I did graduate admissions at Maryland one year I was handed 120 folders from the "rest of the world" - there, as at Michigan, there is geographic specialization by faculty on this task. I read through them all and managed to narrow down the choice set to about 20 strong applications. At that point, I essentially randomized because that was no more or less arbitrary than any other scheme I might have used given the extreme multi-dimensionality of the choice problem. So, I picked the applicant who said in his personal statement that his friends called him "Golden Eagle" and the one who talked in his personal statement about playing Dungeons and Dragons. I kind of intended to follow up on them to see how they did, but I lost track once I left Maryland.
Addendum: in two days, this is #5 on my all time pageview list.
2 weeks ago