In Chapter 1, when Vincent is talking to Reeve, a Deepground soldier gets a lucky shot and hits Reeve, his body collapses to pieces, with Cait Sith popping out. A few seconds later you see "Reeve's" detached head with swirly eyes.
In Chapter 5, segment where you play as Cait Sith is called Solid Cait.
Another amusing shout-out to the same series occures later in the game where you can find Deepground soldiers hiding inside cargo boxes.
Whenever Yuffie is concerned, if you like her antics.
Yuffie: Oh Come on! Aren't you a little concerned? Vincent: Oh... Yuffie.. Long time no see...... How's your head?. Yuffie: Can you at least pretend to be sympathetic!?
Another great one is just after (or before...) your first fight with Nero. Yuffie appears and has a dramatic speech and is trying to sound all cool and awesome. After a short pause, Nero turns around, saying he has to get out of there. Vincent is similarly unimpressed.