What I found I needed to do was follow the instructions given to me by apport when I tried reporting the crash. Apport will only report the crash if you are completely up-to-date on your packages. Make sure you update.
The problem is, there were lots of Maverick packages included on the Natty-Beta disc since the Natty packages were still in the works. The random crashing seemed to be caused by the out-of-date Maverick packages causing weird issues in Natty.
Once I updated, the random crashes went away.
Also, you want to subscribe to the Compiz PPA as well.