From my experience as a dual US/UK citizen, I use my US passport leaving and entering the US and show it at check-in when I'm leaving the UK. I was told to do this by the airline since the US checks passenger manifests and if something doesn't match up when you enter the US it could be a bit sticky.
Entering the US has never been a problem with my US passport, they just ask where I've been and the usual.
The only time I've ever had a real question was entering the UK whilst returning with my boyfriend from a holiday. The immigration officer saw "Walla Walla" as the birthplace and asked where that was (more out of curiosity). I just said the United States and he was amused and let me go through.
