Depth buffer resolution (cel shading)

Hey, I just got the cel shading engine from lesson 37 to work! woo hoo! One thing I noticed- when I''m drawing the black outline, sometimes it draws pieces of lines in the middle of the model (when its suppossed to only draw around the edges). I''m thinking that this problem is due to not enough resolution in the depth buffer, so my question is, is there anyway to increase the depth buffer resolution? either that, or is there a different way to fix this problem? thanks!