Wikimedia Bugzilla is closed!

Might need to split this later, and/or add more details, here's what we know now from it.wp users.

Not logged in user, Firefox 26.0, Windows 7 reports the following.
*When you try to edit a template, the template inspector will look empty.
*When you try to add a new template, the inspector won't provide any suggestions for existing ones.
*When you try to choose an option from the 3-bars menu on the right, none will work (nothing will happen clicking on those), except for the "Switch to wikitext" one.

User:Nnvu, Chrome ver. 32.0.1700.102 m, Windows 8.1, Vector reports having the same issues, plus:
*When you click on a wikilink anywhere in the page, instead than getting the box to edit it, you'll be directed to the linked page (the page will even ask you if you're sure you wanna leave).
*When you save the page, it will stay in edit mode. If you click Save again, you'll get both the save dialog and the loading bar that keeps going. (The page results correctly saved from the history, nonetheless.) 

Nnvu could check the console once, and said that this message
*event.returnValue is deprecated. Please use the standard event.preventDefault() instead.
appeared once the editing page was loaded, while
*Uncaught TypeError: Object #<Object> has no method 'apiRequest' VM189:567
is what he got while trying to type inside the template inspector.

VE will work fine for him:
*if he logs out (but while when he's logged-in, disabling all BetaFeatures, all the gadgets and even blanking .js pages won't still help);
*if he uses FF, as a logged-in user.