I ROFL'd at the blackface comment. And at the risk of dipping my toes in the sucking vortex of meaningless internet debate, I had no problem with either that or the use of the word '******'. (yeah, I laughed at that too)
Yes, '******' can be an offensive word. However, virtually any word can be made to offend someone. It seems to me that people are hell-bent on being hypersensitive and that it is completely wrong to try to try to eliminate any incident ever of using a word or an image that might offend someone. You'll spend the rest of your life trying to be 'politically correct' and to not hurt anyone else's feelings, and odds are, it will cripple your ability to communcate clearly and effectively for you to have to monitor yourself so closely.
This is not to say that continuous use (ergo abuse) of such a word should be tolerated, but as another poster pointed out, I don't recall Yahtzee using it before; therefore, I would argue that if you're really offended by this incident, you're either a) hypersensitive to the word (which is really not Yahtzee's problem), or b) not really a fan of ZP (again, really not Yahtzee's problem) since you are intimating that your enjoyment of the material as a whole is somehow ruined by that one, single word.
You know, if you really are offended, hey, that's your right. Feel free to react by not watching anymore. But considering the rather ironic fact that you made no mention of being offended by the racial slur, I think just maybe you are being a little oversensitive here and are not really concerned with politeness or proper behavior so much as not being offended yourself.