The renderer only works with triangles. Therefore if you have non triangles in your scene they are triangulated at render time.
You faces with a huge number of sides that you are using for curved surfaces. This has to be triangulaed somehow, most likely not in the best way to maintain that curved surfaces. Hence you get a crap result you see in your render.
You need to fix your base mesh. You want to use quad faces that follow the surface flow of the model. Just useing ngons (faces with > 4 edges) is poor lazy modelling that will give you a bad result.
You will also want to use smooth shading which you can activate in the toolshelf (shortcut T)