Polarity classification of words is important for applications such as Opinion Mining and Sentiment Analysis. A number of sentiment word/sense dictionaries have been manually or (semi)automatically constructed. We notice that these sentiment dictionaries have numerous inaccuracies. Besides obvious instances, where the same word appears with different polarities in different dictionaries, the dictionaries exhibit complex cases of polarity inconsistency, which cannot be detected by mere manual inspection. We introduce the concept of polarity consistency of words/senses in sentiment dictionaries in this paper. We show that the consistency problem is NP-complete. We reduce the polarity consistency problem to the satisfiability problem and utilize two fast SAT solvers to detect inconsistencies in a sentiment dictionary. We perform experiments on five sentiment dictionaries and WordNet to show inter- and intra-dictionaries inconsistencies.