Clicking certain dialogs or menus prevents any actions from firing, until it's closed and they fire all at once
A fix is required on Anki's end, and is currently in the works:
https://github.com/ankitects/anki/pull/1643
In the meantime, don't click the gear menu or the reviewer 'more' menu, or open any dialogs, as you'll have to use your keyboard or mouse to escape them. An interim fix might be possible, but it would probably involve either preventing the user from triggering the problematic dialogs or using hooks to close them if they do open using the controller, both of which are hard to implement and still don't allow interaction with affected dialogs.
I've now had two pull requests (here and here) accepted that resolve the issue for various dialogs. These changes can now be observed in 2.1.50 Beta 3. Another pull request is in the works. Next up will be the show info and text dialogs, at which point the issue should be fixed in all the most important places, but if possible it would be ideal to fix the remaining issues down the line.