Are there compatibility problems with buying iPhone 4 overseas?
As long as the iPhone is unlocked and to connected to any network, you can use it in any country. 

You will need to check that if you are buying in the USA and you are getting an iPhone 4 you will need to buy a GSM phone as all Australian networks use GSM after Telstra shut off CDMA, if you are buying an iPhone 4S you need't worry as these combine both networks for maximum coverage.

You may find it useful that some iPhones in some countries are always sold unlocked such as France and Belgium where it is against the law to sell subsidies handsets on contracts.