You are taking all the fun out of this:
The basis of the non-conclusive evidence is a few issues:
1) Planck lengths in some quantum gravity arguments seem to suggest an observer-independent scale, but this is in apparent contradiction to SR as it is currently understood.
2) Discrepencies of the high amount of Ultra High Energy Cosmic Rays (UHECRs) and our knowledge of the transparency of space in terms of the cosmic microwave background radiation (CMBR) suggest that there might be a violation of Lorentz invariance.
3) Discrepancies of 20TeV photons from Mk 501 indicate that according to Lorentz invariance these high energy photons should have disappeared due to pair production when interacting with the CMBR.
There are other more exotic philosophical reasons, but there are reasons to suspect that Lorentz invariance is violated (having more to do with the paradoxes between SR and QM).
Doubly Special Relativity, DSR as it is called, might be a way to resolve the above conflicts (i.e., as Amelino-Camelia, Smolin, and others contend). Fortunately DSR is subject to be tested by 2006 using the GLAST (Gamma-ray Large Area Space Telescope) and AMS program before 2006. If the postulates of SR need modification, we can find out rather soon (hint: if you are thinking of obtaining fame as a young Ph.D. in astrophysics, you might consider this project).
It's 1905 all over again! It could be an exciting time to say the least.
Warm regards, Harv