What problems haven't been solved yet when it comes for instance in rendering,deferred rendering, Volumetric lighting, ambient occlusion or in any other interesting area. When i say unsolved problems, i mean topics in computer graphics that haven't been entirely solved and need serious improvement and maybe new techniques.
I am unsure whether you're talking about realistic image synthesis or realtime rendering, but either way these two are somewhat connected. The biggest issues in real time rendering are really finding good approximations of the algorithms used in realistic image synthesis, and the effective implementation of those, as well as hardware that supports this - think RTX atm. RTX in games however is pretty limited - it is highly biased (you can't even call it a good approximation of the rendering equation for most non-trivial scenes), so we're still at a point where rasterization based graphics dominate. Ray tracing has many advantages however, like its average O(logn) complexity versus rasterization's O(n) (where you can think of n as number of triangles in a scene). Note that this is asymptotic notation, so the main reason why ray tracing is not currently faster than rasterization is that: 1) the current hardware is highly optimized for rasterization, 2) the number of drawn triangles needs to be relatively large to offset the constant (it's unclear whether so many triangles would even be necessary for a realistic representation of shapes). There are however effects and realism which you simply cannot achieve with the "hacks" from rasterization graphics, ray tracing (or more precisely path tracing) is what we're aiming at- when you hit that for complex enough scenes/materials/participating media at interactive rates you've basically achieved photorealism. Now as far as unsolved problems in realistic image synthesis go, there are many. They range from good sampling distributions (the best samplers that we know of currently for CG are usually Owen scrambled Sobol, and some low-discrepancy sequences with blue noise properties - but those usually do not extend as well to higher dimensions), good approximations of the radiance in a scene (there are some recent papers from Vorba and Muller on the topic, they usually call it path guiding), dealing with participating media and complex brdfs (think subsurface scattering), spectral rendering (while there are several techniques for this, you can prove that each of those is bad in some aspect), the theory in general dates back to "Lambert's antiquated framework", and while there have been attempts to modernize it similar to what's been done to other fields in physics for example, the best attempt at that as far as I am aware is Christian Lessig's thesis and the publications following it (which btw do not manage to solve the issue outlined fully). You can say that most problems in realistic image synthesis are actually unsolved - the problem is simply very hard mathematically.