(In reply to Hiroyuki Ikezoe (:hiro) from comment #1)
I often see "A web page is slowing down your browser. What would you like to do?" message, and I am on Linux.
This message appears when the parent process detects that the content process for a tab is spending lots of time stuck in JS. I suspect that this is a separate issue from what Asa is experiencing. If you want to diagnose it, your best bet is probably to run the profiler, recreate the issue, wait a few seconds, and then click on the "Stop it" button in the notification bar, and then dump the profile immediately.
(In reply to Asa Dotzler [:asa] from comment #0)
Testing today's nightly build on x86 on Windows 10 occasionally some UI elements, an extension button, the tab close x button, etc. become unclickable. They don't have a hover state and clicking them does nothing. Restarting Firefox fixes things, at least for a while, then I find something I can't click on again.
Is the parent process hung, or is it just not responding to mouse events? Can you, for example, use Ctrl-L to focus the URL bar in this state?