Once you get the math (and it really kind of clicks all at once), it's not too hard. The problem is that the math has a lot of historical baggage and the ways of translating equations into prose are not the most effective I think.
The whole "uncertainty" thing bothers me. I think there's better ways of expressing this concept to the public.
I am, however, bothered by the fact that QM is not deterministic. Most experiments have ruled out loopholes for a deterministic universe, but it still just weirds me out that randomness is inherent to the measurement of observables.