A multi-criteria data source selection (MCSS) scenario identifies, from a set of candidate data sources, the subset that best meets users needs. These needs are expressed using several criteria, which are used to evaluate the candidate data sources. A MCSS problem can be solved using multi-dimensional optimisation techniques that trade-off the different objectives. Sometimes one may have uncertain knowledge regarding how well the candidate data sources meet the criteria. In order to overcome this uncertainty, one may rely on end users or crowds to annotate the data items produced by the sources in relation to the selection criteria. In this paper, a proposed Targeted Feedback Collection (TFC) approach is introduced, that aims to identify those data items on which feedback should be collected, thereby providing evidence on how the sources satisfy the required criteria. The proposed TFC targets feedback by considering the confidence intervals around the estimated criteria values, with a view to increasing the confidence in the estimates that are most relevant to the multi-dimensional optimisation. Variants of the proposed TFC approach have been developed, for use where feedback is expected to be reliable (e.g. where it is provided by trusted experts) and where feedback is expected to be unreliable (e.g. from crowd workers). Both variants have been evaluated, and positive results are reported against other approaches to feedback collection, including active learning, in experiments that involve real world datasets and crowdsourcing.