The relationship between Dougal and Florence. Despite his grumpynature, Dougal genuinely cares for Florence and is never rude to her like he tends to be with the others.
The original series
In the French version of "Ermintrude's Birthday", Dougal presents a show of fireworks (which almost goes awry), topped off with a rocket for the finale, which, instead of blowing up, opens up to reveal a bouquet of flowers. Ermintrude is ecstatic by this to the point where she even says Dougal's name correctly (whereas Accidental Misnaming is one of her character traits in the French version).
Dougal and the Blue Cat
Dougal surprising Florence with a bouquet of flowers when she arrives in the garden. In the French version, it's mentioned that it's also her birthday.
Dylan's lullaby for Buxton, while Ermintrude and Brian make a bed for the cat.
Mr. Rusty comforting a tearful Florence in the dungeon, especially after the latter sings her sad song.
Dougal managing to wake a comatose Florence up with kisses. When she wakes up fully conscious, she thanks Dougal for saving her life and everyone else's.
Dougal: Oh, Florence, I thought I'd lost you forever! Florence: And I thought I'd lost you, too, Dougal. But you saved my life and everyone else's. Dougal: Oh, stop it. It's what any incredibly heroic dog would do. Florence: Oh. So, you don't want a...little reward? Dougal: Oh, no. I've learnt my lesson. I'm not having anything more to do with lollipops, or gobstoppers, or toffees.
The ending when everyone rides on the roundabout, which is fully restored back to its former glory and functioning once again.
When Dougal is riding the roundabout with Florence, he notices that she is wanting to feed Dougal with a sugar lump, as she still wants to reward Dougal for saving her and those who are trapped in the roundabout. Though he resists at first, he jumps up and eats it from her hand.
The CGI series
Dougal and Ermintrude apologizing to each other in "Kiss and Make Up" after their big fight.
In "The Magic Lamp", after Dougal tries to get his paws on the titular object, he gets into trouble with Ermintrude and Dylan. Realizing how selfish he has been, he uses the three wishes to make up for all the trouble he caused. After using the first wish to clean up Ermintrude's house (which he had messed up while looking for the lamp), he makes his second wish for the two to forgive him, to which Ermintrude and Dylan see how sorry he is and forgive him anyway, proving that he didn't need magic for them to do so.
In "Dylan's Lucky Day", Dougal looks after a lucky clover that Dylan finds, upon finding out that it brings good luck. However, the clover only brings bad luck to Dougal. Later, at Ermintrude's concert, when Dougal gives the clover back to Dylan, the latter wins the number on the raffle ticket he has, but seeing how dismayed Dougal is, Dylan gives the ticket to his friend in appreciation for looking after his own good luck charm.
The episode "Arthur" involves a baby penguin who unexpectedly arrives at Florence's doorstep. Everyone takes turns watching the little guy, but it seems that the penguin likes Dougal best. The usual Grumpy Bear Dougal starts to warm up to the baby himself, and seeing them play together is really sweet to watch.