After some problems with the addon and its configuration, i've got some great support from Martin via e-mail. Now the plug in works with yourls 1.7.3 on my private server.
As another reviewer noted, 1.5 was broken. I was unable to get 1.6 to work, although an older versions served me well for a long time. I just made a new install of 1.7, and I can't get it going, either. I've sent an email to "Ozh," but I've not had a response.
You're having trouble installing the YOURLS server? I'm not involved in the development of YOURLS itself (only the browser plugins), but feel free to contact me: http://binfalse.de/contact/ I'd be happy to help you installing YOURLS :)
The extension itself ist really great and worked like a charm. Unfortunately the version 1.5 is broken and just gives me the error TypeError: gContextMenu is null in line 90. Back to 1.4 which still works.