Data Markets are becoming increasingly popular but are very challenging to deploy and maintain successfully. We discuss some of the challenges related to the success of data markets, focusing particularly on the diverse challenge of assessing data quality. We introduce a novel, holistic approach whereby a blockchain-based smart contract called a Quality Assessment contract allows an actor called the quality assessor to assess the quality of a data asset, provide immutable proof of their efforts on the blockchain, and get rewarded for their efforts proportionally to the value of their quality assessment efforts. We discuss how such an approach could be used in practice to assess the quality of different data assets and discuss some architectural considerations for using a quality assessment contract.