I have been encountering an issue whenever I try to create a new point using the width tool it does this. I am not sure why it is doing that. I think its making multiple points?
It is creating additional width markers. When markers are close to each other you get sharp, drastic, changes in the width.
In CS6 you have to be very careful about where you click and wait for a marker to highlight before you click. It's very "buggy" and inaccurate in CS6 (at least the Mac version is).
Often you see the highlight when the cursor is not actually directly above a width marker.. so wait for the width marker to highlight.
CS6 is not the best implementation of the width tool.. it was new and rushed to market, clearly before it was refined.