Yeah, that makes sense because it's the curves that are close-up that are the problem (takes up more screen space therefore requires more detail to accurately describe vs curves in the back). When you say to adjust the zoom level, do you mean regular scrolling with the scroll wheel, or is there like a special "zoom" render setting on top of just the scroll wheel?
I tried zooming out, rendering, interrupting the render, zooming back in, and rendering again, but I kept getting the same results with the jagged lines.
EDIT: I posted this before I saw Peter's post above. Thanks for the suggestion. I will try it out, and report back.
EDIT 2: Yep, explicitly setting the mesh resolution fixed it. Looks much better. Here it is:

I changed the mesh resolution for the top, bottom, and action pad (dark-gray circle on the right of the controller) from Adaptive to High, and it seemed to fix it. I haven't noticed any slowdown on my computer, but my model's not that complex. All the renderer probably had to do is increase resolution during the tessellation stages of shading which shouldn't increase base-level vertices stored long-term in GPU memory. I'm also working off of a GTX 970, so that should help too.