Looks like I’ve run into Bug #15069. What’s strange is that, I’m pretty sure I remember that prior to activating the Extra settings (with the default setup after installing Ubuntu), I did have some of the fancy stuff that’s apparently provided by compiz, such as the simple Viewport Switcher (or Desktop Wall), but now I have to go back all the way down to None to make dragging windows work. Either the default setup uses some clever hack which was lost when I turned on Extra visual effects, or my memory is failing. There’s a Workarounds utility in compizconfig settings manager, which would seem like a fitting place for a fix for the issue, but there’s none at the moment.
Good Noodles.