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)?
Im going to answer this with a NO. Although some non bitcoin exchanges supports mutual offsetting, for example SGX and CME allow you to offset futures contracts the way you are talking about I'm fairly sure that the mtGOX API only allows you to trade trade on mtGOX. If you need another exchange you need an API for that exchange.
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.