I am a duel citizen of the U.S. and Canada.  I don't have a valid U.S.
passport but DO have a valid Canadian passport.  I live and work in
Los Angeles.  Will I be able to fly from Los Angles to New Zealand and back, for 
vacation, by just bringing my Canadian passport and saying I am a duel
citizen without having any trouble on departure or arrival?  In other
words, the fact that my U.S. passport has expired should not be a
problem, right?   I believe I do not need a visa, so that is not the
issue.  I do not want to lie about where I presently reside.  You do
not really have to research this, so long as you have enough
inernational travel experience to give me a reasonable assurance.

If you've got a valid Canadian passport then I suspect that nobody
cares where you are living.

I am British with a British passport and when I lived in The
Netherlands, nobody ever questioned my place of abode.

Why even mention that you have dual nationality?

Dual nationality should be an advantage but I understand that some
countries require their nationals to give up all previous
nationalities.

Many countries requier that their dual citiznes will enter the country
with that country's passport. I am not sure regarding the U.S. and I
think that is the main question - when Dr. Chou comes back to the US
and enters with the Canadian passport - that might be not entirely
legal.

Well, why not renew your US Passport, just in case?