There is no such thing as a bad word. Mulatto means a person with one white parent and one black parent, which is what Obama is. The only reason it would be derogatory is if you think the mixing of races is wrong. The word 'bastard' is similar. I don't understand how it can be a bad word if there is no more polite word with the same definition. I don't judge people based upon who their parents were. And if the situation calls for it I will use either of those words freely.
A lot of words were used during slavery. There's nothing wrong with the word "mulatto", and the man was raised by his "white" mother and her "white" parents. We can't just claim to be members of whatever race we want; as stupid as the whole issue is, there are rules to it.
Of course there is something wrong with it. We advance as humans and no longer use certain words especially words used back in slavery days. I mean it is 2010 now