It was far from being a one joke series. There were several running jokes going on all through the series. Don't believe it? I'll list as many as I can.
1) Hyacinth's pretentiousness, the primary joke.
2) Her brow beaten husband, Richard, who goes along with Hyacinth just to keep the peace.
3) Her slobby sister and brother in law.
4) Her promiscuous sister who suffers a crisis at the beginning or end of every relationship.
5) The next door neighbours whose nerves are shattered every time they are around her.
5A) The milkman, postman, paper boy, or any other tradesman or visitor to the Bucket residence whose nerves are shattered by Hyacinth.
5B) Anyone unfortunate enough to receive an invitation to a candlelight supper or other function put on by Hyacinth.
5C) Anyone unfortunate enough to receive a telephone call from Hyacinth.
5D) The reactions of anyone with the misfortune to encounter Hyacinth during the times when she leaves the house.
6) Daisy and Onslow's car.
7) Daisy and Onslow's dog.
8) Daisy and Onslow's house, it's furnishings, and state of disarray.
8A) Daisy and Onslow's front garden complete with junk car, miscellaneous debris and the gate that comes away in your hand.
9) The vicar and his wife who try to maintain their spirit of Christian sympathy and charity even though they can't stand Hyacinth.
10) The never seen son, Sheridan, who always needs money and of whom it is hinted at that he is some sort of gay, communist revolutionary to the distress of Richard but to which Hyacinth seems completely oblivious.
11) The well to do sister, Violet, with the husband who seems to come more and more out of the closet each time they are mentioned or shown.
12) The daft old father who keeps escaping from Onslow and Daisy's custody and then goes a streak of mayhem typically involving molesting women, nudity, or re-enacting the war.
13) Onslow's television that requires a sharp smack or special combination of sharp smacks to make it turn on, off, or to change the channel.
14) Rose's telephone conversations with her boyfriends.
15) The person who keeps ringing Hyacinth attempting to order Chinese take away and her responses.
16) Daisy's desperate attempts to get any sort of affection from Onslow.
17) Hyacinth's back seat driving.
18) Hyacinth's singing.
19) Daisy's chipped, cracked, or dirty tea cups that never bother her, Onslow, or Rose, but irritate Hyacinth greatly when she is offered tea in their house.
Those are just the ones that I can think of quickly. I'm sure if I took some time and though about it further I could come up with at least several more that I forgot, so KUA is definitely not a one joke series.