Hi Ozh. I know that this pertains to the Yourls install, not the WP plugin that accesses it, but I can't find what I think is an acceptable way on the Yourls blog. Anyhoos, here goes.
I have the latest nightly updated on my server to see if it fixes the problem. Clicking on the edit action button results in the spinny gif and the icons go grey but the edit slidedown doesn't show up. The share slidedown works, though, and the stats window shows. The only browser that I can it to work in is IE8. Firefox 12 & 13, Opera 12, Chrome 19 and IE9 all do not slide the edit box.