The fact that they apparently don't have to protect your information or tell you the manner in which they have communicated your information (via radio or via computer) is really bad. Also, since I would bet that a large section of the population that listens to police scanner feeds are criminals, this probably isn't a good thing.
If someone were to do automated speech recognition and indexing of these radio feeds, it would be amazingly scary. I've avoided pursuing that angle to delay the inevitable as long as possible.