It's weird, but I saw Mario do the Long Jump in Super Mario Sunshine. I don't completely remember but here's as much as I remember:
Go to Gelato Beach on Episode 8. After you bring the biggest watermelon and the shine appears, stand on top of the juice bar, run and push B to lung, and push A to get the shine. When Mario touches the shine, he should do the Long Jump from Super Mario 64.
Note: This only worked twice for me, and it doesn't move you anywhere.