So I somehow ended up watching a youtube video called Jack and Jill - Nostalgia Critic, and at 14m15s (clip), a joke in the movie is given the spotlight.

Pacino: I used to raise pigeons.

"Jill": Really?

Pacino: Yeah... No, I'm sorry, that was Brando.

Which is met with a fake laugh from Doug, followed by praise what's warrant is questionable at best.

I don't get it. What do pigeons have to do with The Godfather? Does "pigeon" have a second, mafia-related meaning that I'm not aware of? How is this joke supposed to be funny?