I have always wondered about using dual passports. Wouldn't the airline/passport control discover that you've used different passports to check in/pass passport control and board the flight? They may even deny you to check in especially if you need a visa on one of your ordinary passports. How do you solve that kind of problems? Also the immigration in let's say USA may wonder about why you don't have a British stamp in your passport if you're arriving from UK on an American passport...
I am eglible for a British passport, but I haven't applied for one since my Norwegian citizenship has almost the same visa requirements as the British citizenship out in the world.