Continuity mistake: In this episode, it is revealed that Mr. Lucas' first name is Dick; but way back in series 2 ("The Clock"), his first name is given as "James." This discrepancy takes place a few times over the course of the entire show run.
Revealing mistake: When Mr. Lucas gives Mrs. Slocombe the radio mike, it slips down her dress out of reach; Mr. Harman says "It can't have gone down all that far," and he's right: The short cord of the mike is visible sticking out of the dress for quite some time until Mrs. Slocombe herself pushes the mike down (in the appearance of trying to fish it out).
Revealing mistake: When Captain Peacock goes behind the curtain to the hall way to Mr Rumbold's office, you can see that the sets are right next to each other and the other actors are waiting in there for the next scene.
A Change Is as Good as a Rest - S5-E2
Visible crew/equipment: In the opening scene in the board room when Mr. Lucas is commenting on how Mrs. Slocombe is "big in the south," you can see the shadow of a boom mike floating back and forth across the table.
Factual error: Mrs Slocombe's cat gives birth, but the kittens shown at the end are way older than ones who are supposed to have been born just moments before.
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.