Heartless are the darkness remaining from people's hearts. When you kill a heartless it releases a heart
Nobodies are the husks left when a heartless is made, they have no hearts.
So nobodies have bodies and no hearts, but heartless have hearts but no bodies... Whats the deal with that?

Also Yen Sid says nobodies dont have feelings, which is ridiculously untrue. Why are we letting this racist asshole run around spreading his anti-nobody propaganda?

I cant think of any ACTUAL plot holes though.