Those faces missing is probably because of flipped normals. There is a quick and dirty method to fix it in 3ds max, the only problem is the mesh will be twice as heavy. Try the following:
Select the mesh, then Clone it and choose "as a copy". Now you have 2 meshes on top of each other. Select the mesh you just cloned (give it a different color if you want) and remove the Edit Normals modifier if it has one. Now from the Modifiers list apply "Normal" modifier - it will flip the second mesh normals so it will become all black. Now, re-apply Edit Normals on top of Normal modifier. Finally, export both meshes together as one. The gaps on the first mesh will be filled with the ones from the second one.
Ofcourse, thats not the RIGHT way to do it, but it works. Another way is to select only the faces with flipped normals and Detach them, then apply Normal modifier to flip them and then Attach them to the base mesh again.
Or if you have Blender, export the mesh to it as OBJ, and in Blender in Edit mode go to Mesh > Normals > Recalculate Outside, then export the mesh back to 3ds max. It usually does the trick.