Director Displacement: Despite being claimed as "A Wes Anderson Film", there were actually two directors. Anderson directed only the voices while animation director Mark Gustafson did all of the animation (and spent more time on set while Anderson would give directions through e-mail). The film's cinematographer even questioned Anderson's role on the project.
Foe Yay: Rat with Mrs. Fox. "Am I being flirted with by a psychotic rat?!"
Fridge Horror: Mr. Fox said that the tranquilizers were enough to sedate a gorilla. You're probably thinking, "But if it's that powerful, won't that KILL a beagle?" Well, considering that we don't see any of the beagles (except the rabid one) after that...
Jerkass Woobie: Ash isn't a bad person at heart and obviously has a lot on his mind. On the other hand, he's shockingly cruel to Kristofferson, sinking so low as to crack jokes about his extremely ill father with him in the other room.
Memetic Outfit: Ash's very...odd choice of dress, consisting of all-white clothes, a cape and the pants tucked into his socks. Its strangeness is Lampshaded by Mr. Fox, with Mrs. Fox handwaving it as a phase Ash is going through.
The observant will notice him reading a comic book about a superhero called White Mask in one scene (and a poster adorns his bedroom wall), so it's apparently some sort of makeshift superhero costume.
Nightmare Fuel: And how! Bean is outright described as 'The scariest man in the world', and he lives up to the part. His berserking when Mr. Fox's letter arrived is terrifying.
Not to mention Rat. Or Fox and Rat's fight in the electrical storage.
Why has nobody noted down that CUSSING POSSUM and its dead. Hollow. Bulls-eye. Eyes. I would link, but I am still too terrified.
For me, it would be the Rabid Dog's eyes turning red.
Tear Jerker: Despite the character's relationship with Mr. Fox, the death of Rat is quite sad... even if it features a few laughs:
Not a complete tear jerker, but still stronger than Heartwarming, seven words one statement: Ash, I'm so glad he was you.
They Changed It, Now It Sucks: Numerous British people complained about the film's "Americanization", as the humans are British and the animals were American, when everyone was British in the book. None of the Americans seemed to care.
Again, the use of American voices for the animals and British voices for the humans added contrast.
And even made fun of America, in a way, since the difference between the humans and animals is that the animals are "wild", the american accents belong to the "uncivilized" side.
Squick: Taken Up to Eleven with details of how the farmers stink, don't take baths, have horrible-tasting disgusting food, etc.
Uncanny Valley: To some, the realistic fur and eyes on the puppets can be unsettling.
That and the fact that they look just like the animated corpses of roadkill.