Why is it that when I drag a transition, let's say cross dissolve, on to a pair of video clips that sometimes it sits on only one side, sometimes one OR the other, and sometimes it sits accross both clips?
That is because you do not have enough frames on the clips to make the transition.
These are called "handles".. ie spare frames that overlap inside the transition.
I agree with Craig. Handles, or lack thereof, is the most likely cause of the issue. See this article for more info: http://forums.adobe.com/thread/701768?tstart=60
That should be a "sticky". ( How about a shortcut Key)