I took a quick look and, indeed, there are patches with normals not facing out.
Tools to help you fix that...
Shift 1 will toggle Show Normals ON/OFF
f will flip the Normal of a selected patches
Shift 6 will toggle Show Back-Facing Normals ON/OFF to make backward patches easier to spot.
Shift p will turn on "Patch Group Mode" which lets you just click on the middle of a patch to select it, without having to select all the CPs.