In thread Doppler Radar Accuracy, I asked about the velocity measurement accuracy of Doppler radars. The best that could be dug up is 0.1% velocity error for some (classified) military equipment. Interestingly, the 'crossover-point' where the non-relativistic Doppler approximation error equals the Doppler radar velocity error, is when v/c (%) = error%.
Using the 0.1% error, this gives a relative speed of 0.001c = 300 km/s, or a million km/h. Extreme as this speed sounds, it's actually the orbital speed of the Sun around the Milky Way's center. Utterly useless information, but interesting!
If you want to know more about relativistic Doppler shift, scan the download from Special Relativity.