Well, the only thing that I don't get about quantum mechanics is how something can not have a definite state. In the experiment there is a definite state, it just hasn't been observed. So I get quantum theory, but when it comes to actual quantum mechanics I get very stumped very fast.
One thing to note - In many cases where this type of event is mentioned, the truth is that the particle did have a definite state, but the act of observation changed that state without leaving a way to tell what it was before.
So, for things like an electron, the classic example is that you can know where it is or where it's going, but measuring either changes the other, thus you can never know both. This is because it's very small and very high energy (ie it moves at nearly the speed of light), so in interaction with anything else causes big changes.
When a cop uses a radar gun to track the speed of an oncoming car, the energy from the radar waves slows the car down (this is how the radar waves are speed up, which is how the gun figures the speed). However, the net loose of the car is so tiny it's irrelevant, because the car is so much more massive than the photons in the radar wave.
The photons, on the other hand, are so small and gain so much energy from interacting with the car that strange stuff happens. So while most of the photons are bounced back in the direction of the cop, one or two might just pop out the back end of the car and keep on going that way. That kind of thing can just happen at the energy states photons are always in.
Now, when you get to things smaller than electrons and the like (and in some cases they and the other subatomic guys can do it as well) is when you get to the issue of not having a set state.
Of course, in general, having a non-determinable state and having no set state work out to be about the same thing; electrons are just not *quite* as weird as quarks.