Some nice/important points to look for (as I understand them) when watching to a Buddy Rich drum solo:
1. Observe the way (as much as how easy) he crosses his arms and execute all kinds of hand and arm movements so smoothly (sometimes they seem supernatural...);
2. Try to apreciate-and-understand Buddy's phrasings (sequences of drum notes and moves); dynamics over the snare drum and his calculated accents;
3. The more complex and admirable things are, sometimes, hidden from the more obvious/explicit observations (again, try to understand his moves, sometimes you just don't take notice, but impossible things are happening right before your eyes, you simply isn't paying the deserved attention);
4. There's always a brilliant sense of time through the solo (even when it seems all-messy, there's always a jazzistic broken time going on);
5. Observe his left-hand movements and try to understand the incredible dynamics of his left-hand alone (quite amazing);
6. Try to understand his constructions and how Buddy used to mix swing, technique, speed and hand/arms movements' control (or coordination), musicality and everything else in favor of a GREAT and memorable drum solo;
7. Try to vislumbrate (as Buddy said himself) his solos as "well told stories": there's a fine and interesting beginning, an exciting mid, and a phenomenal end, when everything reaches "it's top"). Also, in most of his solos, there's a so long sequence of exciting creative moments that not even one second is dispersed by a boring moment. Incredible. Very consistent phrasing quality through the whole solos.
In other words: try to THINK like Buddy in that particular "drummoment".
Just some advices in order to better understand why Buddy was so one-of-a-kind.
Some (and just SOME) brilliant drum solos that I've cautiously chosen follow below: