Actor Allusion: Rocky yells "FREEDOOOOOOOOM!" when he first flies into the farm. Also, one of the chickens says "I'm not even certain he was American.", a reference to the fact that many people, even in the UK, think Mel Gibson is Australian (he was born in the US, but moved to Australia at age 12). Another Braveheart allusion occurs when asked where he's from:
Rocky: Oh, just a little place I call the land of the free and the home of the brave...
Rocky: No! America!
To top it off, there's also a Running Gag with Rocky finding Mac's Scottish accent incomprehensible.
Rocky: Was that English?
Deleted Scene: One scene that was cut was how Rocky stole a tricycle from a child. In the theatrical release, this causes some "huh?" as to how Rocky was riding a tricycle in the first place.
Executive Meddling: DreamWorks and composer Hans Zimmer (who heads the Dreamworks music department) forced director Nick Park to drop an already-recorded musical score by Wallace & Gromit composer Julian Nott because Zimmer decided his people should do the score (Zimmer has a history of doing this). This was one of many reasons why Aardman would leave DreamWorks in 2006 to go to Sony.note To be fair, however, the score that was released was brilliant.
Another idea for the ending involved a Sequel Hook in which the audience was shown that a second chicken farm is being constructed near the island. It was dropped because Aardman wasn't sure if a sequel would ever be made.
Instead of the door falling on Mrs. Tweedy on its own, after Mr. Tweedy said "I told you they was organised" Mrs. Tweedy was originally going to go on a rant and insult him, causing Mr. Tweedy to get angry and push the door on her. They cut this because it made Mr. Tweedy look too mean. Though in the final film you can still see his arm moving back to his side for a second. You can also see Mrs. Tweedy about to explode with her rant.
Rocky had a wattle on his neck that was removed during production for whatever reason.