Yes, there are changing stations in (nearly) every restroom in both parks (I say nearly because I haven't been in every mens room so I don't know for absolute sure). Disney seems to think that Daddys should enjoy the special bonding of diaper changes just as much as Mommys
. No excuse for Daddys to shy away from the duty.
Most restrooms in DL and all in DCA have large changing stations (flat granite or steel surfaces with a lip - large paper towel 'pads' and toilet paper). I always avoid the fantasyland RRs near the castle (Princes/Princesses) -there's no room for the stroller and it's just cramped.
The baby care centers are the only ones that have padded tables, and you can both go in the changing rooms with the babe - sometimes that's a real help if things are a tad messy or if the babe is rambunctious. DCA's has an adult restroom inside, whereas the DL one does not (you have to go either 1/2 way down Main Street or to the Tomorrowland side of the Plaza Inn restaurant).
If you're staying late - BRING JAMMIES FOR THE KIDLET! We learned that from watching others. Now we make our last diaper change in the parking structure and put DS in jammies for the ride home - then we just dump him in bed when we get home.
Also - in the baby care centers - there are breastfeeding areas, fridges to store expressed/formula bottles, etc. YOu can buy jarred baby food, diapers (also sold at stroller rental) and other misc baby supplies. Pricey, no doubt, but they're available if you need it.
On the boards there have been questions of stroller safety at the parks - I have never ever had our stroller disturbed, nor the things left with it. I'm not stupid - I take my wallet, keys, camera, prescription glasses etc with me, but the bag itself has never been touched. Another side note - the wheel came off our personal stroller one time - a custodial CM saw us, got on the radio, and we got a rental for free. Very cool.
Yikes - I'm at work - I'd better go! We've been going to DL with our now-3-1/2 yr old DS since he was two weeks old, so I've got lots of baby experience!! Ask away!!