I am creating an inflatable pink flamingo in Cycles, and there is an ugly black line at the edge of my mesh that I don't know how to get rid of. Here are my materials and a sample render. How do I get rid of the black lines at the edge of my mesh?
First, it is hard to tell without your .blend file, but I believe I have a two part solution.
Many of your nodes are repetitive and unnecessary. You would get a near-identical result with just the following. Use the Layer Weight node's slider to affect the glossiness (higher value = more glossiness).
Original node setup vs. My node setup:
I assume you have Smooth Shading on, as activated in the Toolshelf. If you do, either return to Flat Shading or add a Subdivision surface object modifier.
To add such a modifier, first go to the Object Modifiers tab in the Properties panel. Select Subdivision surface from the options. Set both the View: value to 2 and the Render: value to 3.
Final modifier settings:
Smooth shaded Suzanne without any subsurf:
Smooth shaded Suzanne with subsurf at 3:
Flat shaded Suzanne: