There's certainly a lot of evidence that compared to RTD, Moffatt's series rarely write or cast black characters, and when they do, those characters generally conform to ethnic stereotypes. Not that Moffatt was blameless (little telly is), but having Mickey - whose characteristics were not black as much as they were simply working class, and Martha - who was a doctor... as prominent main characters, was exactly the kind of racially sensitive casting that all telly should be doing as standard in this day and age.
With Moffatt, though - until Danny there where no recurring BME characters (correct me if i'm wrong), and when characters do appear in individual stories, they have generally conformed to ethnic stereotype (qv - the travel-sick teenager in this series: feckless and disaffected - one of the school's notoriously 'difficult' kids). If you look at 'Sherlock', Moffatt's other headline project, not only is there a massive absence of BME characters, but there is, as
Vintage Paw says, that absolutely dreadful espisode with all the Chinese Triad stuff.