We go to WDW 2x a year and in august we stay at one resort (too hot to switch for us) but in april we always split our stay. We like to start out at a Magic Kingdom resort and then switch over to an EPCOT (our favorite park) resort. We love doing this as it is like having two very different vacations.
It is very easy to switch from one resort to the other. The morning of your switch you just get up, pack your bags, call bell services and tell them where you are going and they will transfer your bags. Then you go off to a park or wherever you choose, and then later go to your new resort to check in.
The cons of this is that you are basically "homeless" that day until check-in time. If you have a young child who needs a nap at a certain time then that can be tough. If it is a rainy day then you need to find places to go so you won't get wet. Some people don't like not having a place for those hours, but it has never been a problem for us. You will also need to check in again, and get new room keys issued. We have ap's so I am not sure how they handle passes or what they do if you are on the dining plan.
You can always request late check-out to minimize the time you are without a room. In april we will first be at The Grand Floridian and I am hoping to make breakfast plans for 'Ohana's at the Polynesian. Then we will spend time at the MK and then make our way over to MGM or EPCOT and then get over to the Yacht Club.
We have enjoyed splitting our stays and it has been fun trying the different resorts. One trip we split our stay at 3 resorts and that was just waaaaay too much for even us!
Jill