During Summer, the Obstructive Bureaucrat tells Dibley that the government solution to Dibley's water crisis is to flood the town, and that, quote, "We will be ready for anything you throw at us." Owen just punches him in the face, laying him out cold.
Owen: He wasn't ready for that!
Crowning Music of Awesome probably goes to the opening theme, which is a rendition of Psalm 23. Its composer, Howard Goodall, stated that he wanted something that could be sung in church, and by God does it work. Youtube has numerous videos of it being sung by various church choirs during services.
You know Alice's "I Can't Believe It's Not Butter" monologue? Emma Chambers learnt it all in one night, much to the shock of Dawn French.
Alice gets one in "Animals" when Geraldine wants to cancel the animal service after the tabloids mock her and David threatens to get her sacked. Alice stands up and points out in a surprisingly cogent way that some people are laughing, not all of them, and if she herself had stopped doing things just because some people were laughing she would never do anything. She turns out to be right, too—on Sunday it seems like the entire surrounding countryside has driven or ridden their animals to church.