One of the things that I can see with new eyes is posing. Posing a character is really important and can make or break your animation. Even if everything is nicely moving, if the poses aren't strong then something will definitely be missing.
By strong poses I mean readable silhouettes and clear lines of action. The character's personality has to be seen in as many poses as possible, if not all. If a character is running because he is scared, you have to pose your character postures so that they clearly show what's happening on that moment.
I remember the work I did for my Hiding Stewie shot. I had lots of comments telling me that the animation was flowing nicely but I could see that something was missing especially in the first 100 frames , and clear and strong poses was one of those missing ingredients.
I hope that my notes make some sense, and to illustrate that , below you can watch my old work compared to the updated version, with clearer poses, and I think that this works better now.