Brian Eastman, the show's producer, saw a three-legged dog in Regent's Park while he was working on the script for this episode. "A few weeks later, the dog was the star of the script", he commented. Brian had hoped to use the same dog for the show, but he never found it again. The search was on for a replacement, and luckily a Jack Russell with a missing leg, who really is called 'Holly', was found and signed up. In real life, Holly is the boss of a pub near Oxford.
The title Three Legs Good is an allusion to George Orwell's book Animal Farm. When the animals first turn out the farmer and start running their own lives, their slogan is "Four legs good, two legs bad". Eventually the pigs move into the farm-house and learn to walk on two legs, and the slogan becomes "Four legs good, two legs better."