Old Tom wants to play with Lucy but is not allowed to, because she has chicken pox. Old Tom goes home and paints spots on his face, so Angela will think he has chicken pox, too. However, instead of letting him play with Lucy, Angela insists that Old Tom stay in bed. He manages to sneak off, but when he gets to Lucy's place, his spots are accidentally wiped off. He races back home and starts to paint them back on, but Angela catches him. She washes them, but they don't all come off - Old Tom really has chicken pox, after all!

Angela and Old Tom are planning to go to the zoo, but the car breaks down. As Angela tries to fix it, Old Tom is accidentally picked up by a garbage truck and deposited at the zoo. There he has adventures in a lion's cage, has tea with the chimps and escapes from two attendants. When he hides in a rubbish bin, he is picked up by a garbage truck again and deposited back home. Angela hasn't noticed he was missing and, now the car is fixed, they drive off to the zoo. To Angela's surprise, all the animals seem to treat Old Tom like an old friend.

In the final episode, Old Tom seems to be back at square one - rejected by much of the community. On a trip to the observatory, Billy causes trouble but Old Tom gets the blame, so he runs off and hides in his old rocket ship. When Billy accidentally unleashes an asteroid which threatens to destroy the world, Old Tom takes off in the rocket - with Lucy and Angela - and manages to avert the catastrophe at the last minute. Old Tom lands the rocket back on Earth, in the middle of Lavinia's party, where he is finally appreciated for who he is - wild, free-spirited and occasionally berserk - but always a hero.

Old Tom overhears Lucy and Angela complaining about Billy, and mistakenly thinks they are talking about him. Devastated that not even his best friends really like him, Old Tom runs away from home and joins a circus. There, he is immediately accepted and told that he is not the 'no-hoper' he thinks he is. With the encouragement of the Ringmaster, Old Tom learns that everybody has a talent, and his talent is to make people laugh. Meanwhile, Lucy and Angela search the town for Old Tom and eventually find him in the circus - just as he is doing his act. They clear up the misunderstanding with Old Tom, telling him they were always proud of him and always will be, and he returns home with renewed faith in himself.

When Old Tom is finishing his bath, his favourite bath toy - a rubber duckie - goes down the plug hole and gets stuck in the house's plumbing. Old Tom tries to retrieve the toy, but ends up soaking Lavinia, who has come for tea. On Lavinia's advice, Angela calls a plumber who, with Old Tom's help, tries to fix the problem. But he, too, accidentally soaks Lavinia. Tired of all the drenching, Lavinia leaves, only to be soaked again when the blocked garden hose explodes, flooding the house - but finally releasing the little rubber duckie.