Assuming the first guy has truly pathetic systems and is plain inefficient, what can one do?
Things actually might be ok, but I am wondering about a worst case situation.
I've never seen one go wrong . . with the exception of the one time when someone attempted to hijack one of my domains at the very moment when I was attempting to transfer the same domain. Strange how that worked, with me approving the hijacking. (Old system + waaay too many domains at waaaay too many registrars. I lobbed a few nukes and the innocent thief promptly surrendered the ill-gotten domain.)
Assuming the domain is, in fact, unlocked and the EPP code has correctly been passed and correctly entered by the receiving registrar, and the EPP code wasn't otherwise somehow hijacked in transit, there shouldn't be a problem.
I'd double check the WhoIs record both at the losing registrar's site and at the receiving registrar's site, just to confirm it's unlocked. Also, go back into your account at the losing registrar to confirm the status of the domain, locking, etc.