Were your face normals correct in blender before you exported it ?
Turn on normal display in properties panel (shortcut N) when in edit mode.
You can flip the normals of selected faces with W / Flip Normals
The normal of a face is basically telling the direction to which your face is pointing.
When you are in Solid display by default you don’t see when anything is wrong because in Solid mode both side of a face are drawn and lighted.
Now you press N , scroll down to “Display” and enable “Backface culling” and then you’ll see immediately if one of your normal is wrong as it will look as if that face is invisible (due to the normal pointing in the wrong direction, leading the engine to think it’s a backface).
Usually when you look at your model and see some very odd darker faces, it’s usually a good hint too that you have wrong normals for them.