Although "dumb" literally means unable to speak, I don't think anyone has used it in that way for a long time. It just means "stupid" these days. By contrast, "retarded" is still used to refer to mentally challanged people, and is, I believe, still the medical term. Therefore, calling a stupid idea "retarded" is somewhat offensive, whereas calling it "dumb" is not.
As for racial slurs . . . I don't like hearing the word "retarded" or hearing someone called a "retard." But, I am furious to hear someone called the n-word, unless its between friends, or to prove a rhetorical point. (For example, I used it in a private conversation with another attorney regarding a voting rights violation. I commented that the people down there "don't care if them n-ggers vote." What I meant, and what the other lawyer understood it as, was not a slur against the black people whose rights had been violated, but a slur against the rednecks who had interfered with their ability to do so. What I was saying, basically, was that the individuals involved were the sort of people who call black people n-ggers)
The problem with racial slurs is not that they are just words. They are, of course, just words. Nor is it that they are "bad words." The f-bomb is a bad word, but, in most circumstances, it is just a lewd, crude word. It is not a word intended, and used, to wound someone. You might call them a motherf-er, but you probably don't mean that they engage in sexual congress with their mother. You're expressing contempt and rage, but you are not trying to drive a nail into their heart. Calling a black person a n-gger doesn't just express anger, or contempt for their behavior . . . it is dismissing them as person, striking out at what they are, and using the most hurtful thing you can say. Its dehumanizing in a way that "motherf-er" isn't. It says, "you're not a person, you're just a n-gger."