When the series was made, the word pleb was in much more common use than it is today (excluding the last month or so) – so I doubt the use of the word caused any concern.
At the time, I regularly used the phrase ‘I’m just a pleb.’ – meaning one of the masses; and in the 70’s my peers would also use the term in everyday speech. Rarely was it ever used (as by Mr Mitchell) as part of an insulting rant against those of lower class.