I thought this was an interesting story. The short version is a cop claimed that he heard a car more than the length of a football field away behind him (he was parked parallel to the highway) speeding. There was other traffic on the road but he claimed that he only heard the car that he ticketed. The officer did use a radar gun to confirm his "bionic" hearing, and found that the car was going 42-46mph in a 35mph zone, but upon appeal that evidence was thrown out because the officer forgot to include the model number of the radar gun in his report. A court then still upheld the conviction based on only the hearing evidence and after two years of court cases an appeal finally found that sounding to fast is not sufficient.
The full story that I read is linked here:
http://autos.aol.com/article/audible-speeding-tickets