This is actually supposed to be a closing? That's appalling. What possible comeback to you have if they leave the place in rag order? On the basis of what you've said, it sounds to me as though your solicitor is out of order, and you *must* carry out a final inspection when they leave and ensure that any junk left / unacceptable state is fully dealt with.
Having spent the entirety of this weekend cleaning our "new" house so that I'm no longer afraid to touch anything without a bio-hazard suit, I can't sufficiently stress the importance of final inspection (we did get a minor rebate, though nothing compared to the Augean stables state they left the place in), and if the final inspection is post-closing, then the funds must still not be released from trust until *you* say so.