Counts of citations to academic articles are widely used as indicators of their scholarly impact. In addition, alternative indicators derived from social websites have been proposed to cover some of the shortcomings of citation counts. The most promising such indicator is counts of readers of an article in the social reference sharing site Mendeley. Although Mendeley reader counts tend to correlate strongly and positively with citation counts within scientific fields, an understanding of causes of citation-reader anomalies is needed before Mendeley reader counts can be used with confidence as indicators. In response, this article proposes a list reasons for anomalies based upon an analysis of articles that are highly cited but have few Mendeley readers, or vice versa. The results show that there are both technical and legitimate reasons for differences, with the latter including communities that use research but do not cite it in Scopus-indexed publications or do not use Mendeley. The results also suggest that the lower of the two values (citation counts, reader counts) tends to underestimate of the impact of an article and so taking the maximum is a reasonable strategy for a combined impact indicator.