Being an Oregonian, I especially loved the slugs (our state bird ya know).
The animation technique pays homage to claymation ala Wallace and Gromit.
London sets the stage for exaggerated class differences, with the Kensington Rat (Tony Blair type) finding his familial roots in the sewer (sexy girl rat).
As Dawn commented, you need to be up on your movie allusions to fully track some of the humor.
For example, the "daddy, I want a pony" meme is something of a joke around our house, ever since the Willy Wonka makeover (Johnny Depp & Co.). That meme pops up here with a vengeance at one point, as we satirize the villain, a Toad of Toad Hall type, and his spawn.
The behind-the-scenes puppet master toad is stereotypically driven by some crackpot scheme for world domination, which all too predictably includes "ethnic cleansing" in some dimension (i.e. let's get rid of the sewer rats).
Everyone wants to deprive the UK of its native street smarts it seems, including the French (the mime frog was a nice touch).