I am not a lawyer but have had occasion to hear this discussed. It can depend on the state where the conversation takes place AND if both parties are in the same state.
Often the law states that as long as ONE party knows the call is being recorded, its ok to make the recording however this can change.
I don't agree with infringing on someones privacy even if the law said that was OK, thats not right to do to someone, no matter how bad your relationship is with that person. However that is a seperate issue from his racism. I don't think his son outting him to the world as a racist makes it ok that he mis-used his trust like that.
Whatever personal problems Dog has, his son sounds like he has his own issues that he would do that too his Father. It was a very manipulative and back-stabbing thing to do.