Web clipper is not working for me either. Tried signing out and then back into Evernote and even Safari. It seems to be opening a tab which I think says that Evernote is successful but closes it so fast I can't really read all it says. And no new note is added to Evernote.
I even uninstalled and then reinstalled the web clipper, then even updated it to 6.12.4 but still have that troublesome dot on the bottom left of the icon which has indicated previously that it isn't working, and it isn't. Luckily Chrome is working.