Was the Professor Gates arrest the result of a well orchestrated publicity stunt, or are the Boston Cops inept?

Neither. Professor Gates has, in the past, expressed a strong dislike for 'Whites'. As you noted, he is quite proud of his Bigotry! He simply 'lost it', during that incident. His release was nothing less that that the Elite Ruling Cl of his State, having Absolutely no wish to present to their people the evidence that they have for so many decades condoned, nurtured, and promoted such a blatant Bigot within their community, especially one who is an advocate of physical violence!