Throughout the day, the Jurassic Park Discovery Center has hatchling raptors. If you're there when it happens you can volunteer to give it a name. If you do, they'll give you a certificate for being a proud mama.
If it's a slow day at the MIB ride, ask a crew member if you can get a tour of the immigration room.
I saw someone doing this on my last trip, and now I finally know how to get in on it!
Any of the merchants that sell fountain drinks will give you a free ice water if you ask. Most indoor eateries will also fill up your water bottle or thermos.
Buy something in the park that you don't want to carry around? Ask for package pick-up and you can stop at Guest Services near the front of the park before you leave to pick up your purchases.