Animations not displaying correctly.

I am trying to get the animations from this model (http://www.blendswap.com/blends/view/25313) to show up correctly. When the animations play, pats of the model disappear and other parts animate oddly. What is causing this? I am really good with Maya but have never used blender, so my typical maya tricks of freezing transforms and things like that wont work. And since I have no experience in blender I don't even know where to look in the UI to find those sorts of things.