In this paper we look into the use of crowdsourcing as a means to handle Linked Data quality problems that are challenging to be solved automatically. We analyzed the most common errors encountered in Linked Data sources and classified them according to the extent to which they are likely to be amenable to a specific form of crowdsourcing. Based on this analysis, we implemented a quality assessment methodology for Linked Data that leverages the wisdom of the crowds in different ways: (i) a contest targeting an expert crowd of researchers and Linked Data enthusiasts; complemented by (ii) paid microtasks published on Amazon Mechanical Turk.We empirically evaluated how this methodology could efficiently spot quality issues in DBpedia. We also investigated how the contributions of the two types of crowds could be optimally integrated into Linked Data curation processes. The results show that the two styles of crowdsourcing are complementary and that crowdsourcing-enabled quality assessment is a promising and affordable way to enhance the quality of Linked Data.