Okay, thanks to _Danny_B_ for pointing out that this completely breaks with right floats. Floats will be needed to work nicely with floats, but it's impossible to get floats to position precisely across browsers, that I can see. I think the German way of doing it, with the edit link on the left, has gone back to being the best choice, although it might use these tabs if people like them more than the bracketed link. (I'd sooner stick with the more traditional brackets.)
Magnus, by the way, your script doesn't seem to work properly in non-Firefox browsers. It highlights the sections, but then refuses to un-highlight them when you hover out.