The site does not handle payments at all.
Each user has a profile (payment methods they accept, comments from other users, etc) and a list of other users with whom they trust enough to trade with or run a tab for and up to what amount.
Bids and asks are placed like on MtGox. They will only be available to users who are on your trusted list.
When an offer is accepted the system will record the obligation that each participant has to the other. Participants settle and the obligation is cleared when both report payment.
When there is no hurry and obligations sit for a while there is a chance they will be reduced by trades in the opposite direction. This would save on fees or hassle. Furthermore, traders with mutually trusted parties can have their obligations netted out.
Since we're already dealing with the trust issue it might be easy to get an options market going here too.
People with no trust could even prepay to any well trusted member. Noob sends me $100 on PP. I create an obligation to pay him $100 and now anyone who trusts me will be willing to sell him up to this amount in return for that obligation because they know I'll pay it.
If anyone is interested in developing something like this I'd love to help, but I can't do it myself. I don't have any ideas on monetizing, but I'd still be willing to front some money to someone who is sure they can do this. Suggestions for a name that gets the idea across are welcome too.