I hav had similar issues in the past, but have found a way to work around them with the work arounds being consistent.
For one, when I add a div it doesntnalways land where expected. The workaround is to create it as close to where I want it to be, then outdent it or move it up or down.
I've also noticed that the div that appears to be the one selected, really isn't and that's why changing the name or other properties affect a different div. I've noticed that I sometime have to click twice to actually select that div. The first click highlights it, bit in a lighter color. The second click highlights it in the dark blue.
After making the change I have noticed it won't keep if I click apply or move on to another tab. I first have to click to another div for the new name to show up in the tree, then back to the new div, again sometimes having to click twice on each one. If everything hold, then I know it's taken and I can move on.
Also, and in other extensions, the first click of androp down menu selects the first option. I have to select a second time.
Some of these things happen in Dreamweaver dialogs too, not just web assist extensions. For example, if you change the name of a text field without clicking out of it, or pressing enter, the new won't keep. Maybe there's amconnection there.