Challenges of Offline Rendering
Since you've used the "path tracing" tag, I'm assuming you're thinking mainly about light transport. At SIGGRAPH 2015, there was a course on the topic of path tracing in movie production that may be interesting:
https://sites.google.com/site/pathtracingrevolution/
Some of the presenters point out unsolved challenges towards the end of their presentation, for example see the second to last slides in the presentations from Alexander Keller and Johannes Hanika.

Then there are challenges in rendering that are not necessarily tied to path tracing but also present in game engines. Triangle meshes as an approximation of smooth solid surfaces are one, the use of shading normals or even worse, bumped normals have been pointed out as a source of artifacts a long time ago: "It's not really a rendering bug, you see..."