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.
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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.