I imported the model into 3ds Max, resaved the model in smd format, imported it back into 3ds Max, exported it to Maya 2010, and then copied the skinning to the model within Maya. That's all.
Regarding the polygons, you made a mistake; I have nothing more to say.
Added 41 minutes later
I understand the polygon issue. The character's jaw is only 1 polygon thick, and polygons have a property to be displayed either on one side or on both sides. In my case, only one side of the polygon is displayed. How can I make both sides visible?
Added 20 minutes later
Or, alternatively, how can I change the direction in which the polygons are displayed?