While reviewing posts today on the review page, I upvoted a question and got the "share a link" dialog. It would not go away. Clicking "close" did nothing, and reviewing other posts did nothing.
Update:
This happened again today, and I noticed that it seems to fail when more than one of these is open at a time (I ignored the first one and tried to close the second - failed). Perhaps that has something to do with it?
Update:
Reproduced again today, with excatly two of these open and on-screen. Clicking close in the second one closed the first one, and the close button then became useless.
Update:
When multiple questions are opened in the "review" state, upvoting one of them causes the box to appear in the others.
Update:
This seems to apply to the "Vote to close" dialog as well (one dialog, several questions "opened" for review) - clicking vote makes it look like it is submitting, and it never goes away (but it does submit the vote).
Update:
After closing one like this and reaching this buggy state, no more of these will open.