Does mtGOX allow for buying on one exchange and selling on another through their API? Can the mtGOX API be used to buy on one exchange and sell on another, if so, how? (An example api call/url etc would be great)?
The Mtgox API can be used to buy or sell on Mtgox. To buy or sell on another exchange you'll need the API of that other exchange.

More information about the Mtgox API can be found at https://en.bitcoin.it/wiki/MtGox/API.