Create browser-based update notification mechanism
The check.torproject.org update notification has several problems. It's web-based, overloaded, and unmaintained.
From a usability standpoint, I think I like the idea of an ever-present notification ribbon/toolbar thing on all windows rather than a popup that appears only when the check interval expires, so long as it can't be confused with something from the content window.
Note, we'll also want to make sure that such a ribbon does not change the size of the resolution values from your CSS + window.screen patches... This might actually be fairly tricky in practice, due to there not being a lot of slack in the current window sizing code in Torbutton ( https://gitweb.torproject.org/torbutton.git/blob/master:/src/chrome/content/torbutton.js#l4358). See also #6146 (closed), for example... We could handle this issue by simply giving a larger buffer for maxHeight in that function, though.
Another option could be some sort of icon hint in the Toolbar (for example, Google Chrome places red up arrow over it's 'menu vent'), but that is even more likely to get ignored.
In either case, the notification should provide a link to the TBB download page, and should pass the OS and architecture to this page in the form of an anchor/fragment (see #4238 (closed)).