Moto_man is right, the issues are precisely why one has an escrow arrangement --very common for far more at stake. If there is ultimately disagreement the agreement provides for interpleader- the property goes to court and the parties litigate; the agent follows the court's direction. The escrow agent is usually held harmless by all (and presumably has insurance).
I think it is a great idea, and just mentioned it elsewhere. I’ve had occasion to deal with this in all kinds of property transactions for myself. You can never be too careful, but the escrow system solves a lot of problems. Would I want to take it on as the escrow agent? No. But, done at the right scale, with the right people, it could be good for us citizens.

