If I'm going into a bar the first thing, either at the door or outside the venue, depending on the volume, I look for a solid tempo. As I hear more I'm looking for how well he/she is playing to the song and with the rest of the band, and how it feels: does it feel natural or forced? Then I listen for tuning, especially the snare and kick, and finally how the fills fit in the context of what's going on.
If it's me playing and I see another drummer or any other player or someone that runs a studio come in that I hold regard for, I ask myself if what they hear is someone they would want to play along with or record with.
When I go to shows and hear a "Pro" player, I notice some very subtle things in their feel and timing. I've seen John Hiatt with Kenneth Blevins playing drums and it just blew me away. I say someone like that has 'relaxed precision'. Like Jim Keltner or Stanton Moore, what a feel they have. Not everyone has it and it seems it takes a long time to get there.
Thanks for the responses so far, keep 'em coming.