I did an initial literature search and feasibility test for a 3D special relativity simulation.  There are a few projects out there that are already trying to address the same problem, notably:

http://www.anu.edu.au/Physics/Savage/RTR/
http://www.anu.edu.au/Physics/Searle/Obsolete/Seminar.html
http://lightspeed.sourceforge.net/

It's straightforward to set up Lorenz contraction in a 3D Java program, but as Savage and Searle point out in http://www.anu.edu.au/Physics/Searle/paper2.pdf, pure length contraction is rarely seen alone, and indeed is not the most striking visual phenomenon at relativistic speeds.  Other effects that lead to nonlinear aberrations are caused by the non-negligible travel time of photons.  In fact, they chastise Gamow for ignoring this in the Mr. Tompkins story.

While it could be straightforward to implement pure length contraction and time dilation, this is at best an incomplete picture for relativistic speeds.  I'm not sure how much work would be involved in handling the non-negligible travel time of photons and nonlinear optical aberrations (and other effects like headlight effect, etc).  The places where I saw potential for improvement over the Savage et al implementation were:

1. Make it easier to download/launch for many platforms.  Current implementation requires Windows and a graphics card with a programmable graphics processing unit.
2. Improve the user interface, easier controls
3. Add in-simulation measurement tools
4. Add a more everyday-life scenario (like streets, trees, cars, houses) instead of an abstract futuristic environment