I have a pretty long list, since i often am picking bats for you guys as well.
1. Willow Quality, is it good and appropriate for the model. personally i like a butterfly or two on my bat and specs are also a plus for me as generally these bats are pretty good with performance.
2. Pickup, is the bat picking up well? Must be light weight unless asked otherwise (believe me i get request for toe heavy bats too)
3. Weight, it must be as needed coz despite good pickups, heavy weight can have its impact in the longer run, especially on the back.
4. Profile, i like middles in the middle and too low or high are not preferred.
5. Handle, the shape, the no of pieces and the thickness.
6. Edge Size, A lot of people look for large ones.
7. Toe and Shoulder thickness, it is pretty crucial in the longer run.
8. Ping, Obviously, as it is what matters in the longer run though it will really be known how the bat performs once it is properly used.