"Region stabilize" effect to focus on stabilizing one object in an image
One of my favorite effects in Avid, "region stabilize," allows you to select the pixels that you want the stabilizer to analyze when creating the stabilization data. So if you have a shot of a flag whipping in a hurricane, but there's a rock in the shot that's still (or ought to be, if your camera wasn't bouncing around,) you draw a square around just the rock...and the stabilizer looks only at the rock's movement within that square as it stabilizes the whole image based on those pixels' motion. Rather than the current method, which looks at the whole image and tries to stabilize everything...usually meaning, in the flag example, that it will try to stabilize the whipping flag and end up making the shot shakier than it actually is as it follows the motion of the flag. The effect is also keyframable in Avid, so if a camera flash or a person walking through the shot threatens to throw off the stabilization tracking, you can just throw the "area of interest" to another point or off the screen altogether during the problem frames. Getting that functionality into Premiere would help with an awful lot of stabilization issues.
Matti Heimonen commented
One of the things I miss from my Avid days, for sure!