First off… Turn off ‘Double Sided’ in the ‘Object Data’ Tab… It’s between the ‘Modifier’ tab and the ‘Material’ Tab.
Icon looks like an upside down triangle. The option is under ‘Normals’.
You’ll be able to handle more polys and sculpting will be MUCH smoother.
Your problem is that many of your normals are inverted. Tun on Face Normals in the Mesh Display section of the properties panel [keystroke ‘N’] and you’ll see that all of the normals on the right belt are facing into the mesh. There are some edge polys that face inward as well.
For whatever reason, ‘Make Normals Consistent’ (ctrl+n in edit mode) doesn’t solve the problem.
Here’s how to fix it:
In Sculpt Mode, decrease PREVIEW subdivisions to 0 in the Multires modifier.
Go in to Edit mode, turn on Display Face Normals. It’s in the Properties panel (N key in 3D view) under ‘Mesh Display’ section.
Those little lines show you the direction of the normals. They should all be facing outward.
It may look confusing with all those lines, so select the top loop of polys and hide them (H key).
You’ll see that the polys underneath point straight up into the geometry. This is no good. They need to point out from the interior.
Select the offending polys and flip them using Ctrl+f and 1st option Flip Normals, or the button in the toolbar, ‘Flip Direction’ might be faster.
Your going to have to hide polys, examine normals, flip as needed, unhide (Alt+H), repeat.
Luckily this mesh is at its base very low poly, so it shouldn’t take too long to go through. You did remember to set Preview subdivisions to 0, didn’t you?