Mel Gibson is clearly in the grips of personal turmoil and bigotry. Are his drunken rants relevant to the offense of drunken driving with which he is charged? No. Did the LA Sheriff's Depratment show leniency toward him by suppressing them? Not really.
The sheriff's department is charged with keeping the peace. Would broadcasting irrelevant hate speech by a public figure make their neighborhood more peaceful or less peaceful? I'm guessing the remarks would stimulate unnecessary controversy. So why get into it?
At some point Mel has to face up to his prejudices and acknowledge them publicly if he can't bring himself to get over them. But it's not the job of the sheriff's department to borrow trouble by relaying his unfortunate sentiments in the context of an investigation in which they really play no part. If Mel had gotten juiced and run his car into a crowd outside a synagogue while shrieking his slurs they would reasonably have a place in the public record. And if some Bozo no one ever heard of mouthed off with racist bullshit at a traffic stop no one would care at all.