Big-Lipped Alligator Moment: In the 1978 special "Happy Returns." The store is celebrating Mr. Grace's birthday; the staff have rehearsed an extended musical number to perform as entertainment. At the last minute, they have to perform something else, so they break into an impromptu version of "Steppin' Out". Okay. Suddenly, Mr. Grace appears, holding a puppet body under his neck, singing a song about "bread and drippin'" which contains only a couple of intelligible words in it. This weird little ditty doesn't fit with the other music at all, and turns Mr. Grace from guest of honor to entertainment with no explanation. Then, the staff segue into "Happy Birthday to You" as if nothing had happened. The actor who played him was quite literally on his last legs, but wanted one more scene to say goodbye. This was that scene, with him wheelchair-bound and barely able to speak. He died shortly after filming. Crowning Moment of Awesome if you ask this troper.
Cargo Ship: Mr. Mash's somewhat disturbing attitude towards the female mannequins.
Germans Love David Hasselhoff: Although the show was popular enough in Britain, it is well known as one of the most unexpectedly successful transatlantic transplants, being very popular in the US thanks to years of reruns on PBS..
And in the State of New South Wales in Australia (The ONLY state!) because until quite recently, the biggest department store retailer in that state was called, you guessed it, Grace Brothers.
The Sequel series, Grace & Favour was shortlived in the UK, but it was much better received in North America with it being retitled, Are You Being Served? Again!.
Replacement Scrappy: Virtually every replacement for a main character. Mr. Grainger's four replacements, Mr. Spooner replacing Mr. Lucas, and Old Mr. Grace replacing Young Mr. Grace. It could be argued the only exception was Mr. Harman replacing Mr. Mash.
Uncanny Valley: Every now and then, Grace Brothers will get some kind of mechanised dummy as a marketing gimmick; inevitably, the dummy is quite creepy and falls squarely into the valley.
Values Dissonance: In 'The Punch and Judy Affair', all the men protest when Mrs. Slocombe wants to play the policeman, finding the idea completely outrageous. Women were not integrated into the main British Metropolitan Police Service until 1973, which is just before the show started running.
While not considered that out of the ordinary during the '70s, the number of casual jokes regarding molestation, sexual harassment, and rape in earlier seasons would get side-eyed hard nowadays, if not considered downright offensive, particularly regarding the repeated accusations of Captain Peacock harassing Miss Brahms, throwing their power imbalance into the equation. It's probably telling of how societal views changed even during the show's run as those kinds of jokes were phased out near the end of Mr. Lucas' run and Captain Peacock changed from a Memetic Molester to simply an amorous guy who gravitated toward pretty young girls but didn't get beyond (usually failed) attempts to chat them up.