I cannot start closing question as duplicate from mobile Safari (tested on both iPhone and iPad). When I choose close as exact duplicate and paste url of the question the dialog freezes. The text is blured - both url and former text is visible and question's preview doesn't load which causes that vote to close button is still disabled.
It does in fact work, so long as you register a "keypress" in the close input box.
That is, if you paste, that's not a keypress.
So enter a space at the end of the URL after pasting (this won't harm anything) and everything should work as you expect.
I was indeed able to close this question as a proof of concept on my iPhone.