So again, the idea is to create this app, that would function in a p2p network. Once installed:
a) You would have a wallet in that app.
b) You can set the bid/ask price in the app.
c) When you install the app on your cell phone you can report your geolocation (so buyers and sellers can locate you).
d) When someone sends bitcoins to the app's bitcoin address(or when bitcoins are sent from that address), a trade is reported to the p2p network.
e) Clients calculate the price from the transactions reported @price reported.
Again, we should split the exchange operation from the fiat <-> digital conversion operation.
Your idea is like localcoin but with much faster updates.
Your app would basically allow people register that are willing to trade fiat to/from some digital representation of the fiat. You can then buy digital dollars for real dollars.
A person could walk around with $50 "float" in their wallet and register that they are trying to sell $50 cash for 50 digital dollars from some mint. It would scan if there was anyone nearby willing to trade. If not, the trade remains on the system.
The mint could operate in $10k or more transactions, so much easier for the mint. It could operate anywhere in the world, and for large transactions like that, it would be worth it for people to collect mint coins and return them as a bloc.
The user could set areas where they are willing to be broadcast. This would allow some privacy, rather than constantly updating your current location to the system.
Effectively, you would say that you are available when near home or near the city center. If you pass free wireless and are near one of your available locations, it would update, and updates remain active for say 30 mins. It wouldn't do constant updates of your exact location, just say "near some landmark".
Your system does work for direct BTC to fiat conversions, but keeping the exchange and minting separate allows the exchange to be more sophisticated, and much more liquid. Taking a while to confirm a dollar to digital dollar isn't as big a deal as delays when the BTC to dollar exchange rate is moving fast.
Ofc, the app could offer both system, so maybe not really a big deal. If you set it to poll the exchange, then you get most of the benefits anyway. Sell orders and buy orders are for people who are offline.
It has the disadvantage that there is no way to confirm orders. The face to face nature of the transaction means that the buyer of the fiat currency is guaranteed the money. However, the BTC buyer would have to wait for confirms.