Question: Does anyone know why Wendy Richard (Ms. Brahms) is the only one not wearing blackface for the musical number at the end of the episode?
Answer: In Britain, there was the show Black and White Minstrels which was very popular until the late 70s. The men were all blacked up, but the women weren't - hence Black and White Minstrels. It's been a while since I saw the episode to know if Mrs Slocombe was blacked up as well, but technically she shouldn't have been.
Answer: In minstrel shows there was also a stereotype of black men preying on white women, so that's probably why she was not in black face. Also, Mrs. Slocombe is in blackface because she is an older, stout woman and she fits the "mammy" stereotype.