The character of Terence (Sean Penn) says no dialogue in the whole film. He only did humming, grunting, and opera singing.
(at around 10 mins) A nod to Steve Jobs: a bird, wearing a black turtleneck sweater, is working at the Apple Store in the background, as Red is trying to cross the street. He holds an apple to his head.
(at around 4 mins) In the beginning of the film, when Red asks the two birds what they rate the birthday cake he delivers, he asks how many stars out of three. This is a reference to the game. The highest score you can get is three stars.
Earl Pig, voiced by Blake Shelton, has a tattoo that is nearly identical to Shelton's real tattoo, the only difference being instead of hooves, the tracks are bird feet.