If I were to sell property in a different country and the buyer were to pay me in bitcoins, would there be any taxes to pay? And when trading in the bitcoins for UK GBP, would there be any taxes to pay then?
Whenever bitcoin is bought, sold, or traded, there are tax impacts. When it comes to taxes, the Internal Revenue Service has ruled that bitcoins and other "convertible virtual currencies" are "treated as property" and not treated as currency. Virtual currencies are property for tax purposes. That means, you'll have capital gain or loss when disposing of virtual currency. Business transactions as well as selling properties in bitcoin are subject to all the normal rules for sales tax, withholding, and information reporting.
Yes, don't mess with the IRS
Obviously, you talk about only the US citizens (the IRS is the US tax agency) since in other countries and jurisdictions there can be different regulations. That said, if you use Bitcoin for trading purposes (i.e. when you sell it for fiat, say, the US dollar, and vice versa), I guess you should not declare every transaction (i.e. trade) you make. You just calculate how much you earned (lost) in total and declare that amount to the IRS once a year, and, correspondingly, pay the capital gains tax (or whatever) once a year as well (provided you booked profits in the first place, of course)