We like split stays.
One trick is packing correctly. It is also a help if you have a car.
The downside is the time it takes. It always takes us some time, but it is still very doable.
One aspect with Disney is 'packages'. You are much better off doing the second stay as a room only booking. If you are attempting a split stay during free dining type promos- you kind of miss the free dining at the second resort. (You may however find a bigger % off deal).
We once did a split where our first night was room only, and the second part was apackage. It was great, except that we HAD to go to the second resort to get our tickets/meals credits. It forced me to take a relaxation day. Normally I'm eager to get to the parks.
The only other considerations are that if you have WDW transfer stuff then it won't arrive until after 3 or 4pm. Also, you can't really transfer perishable foods items or medicines- like anything you must keep in the fridge. (cookies would be fine) Your stuff stays in normal temps AC controlled areas- but not in a fridge. To get around the lugggage delay, you can stow things in the park lockers, but that's never appealed to me. You could also wear your bathing suits under your clothes all day.
I disagree about making it three nights. I find one night transfers to be quite worthwhile under the right circumstances. If you are just doing one night all you need is one msall overnight bag - more than that and you have to unpack. I've stayed one night at a value resort and the rest at a deluxe. We do that sometimes if we have a very late flight and a car. More than once, I was going to fly in on a Friday, but discovered we could go down Thursday night- stay at a value/offsite - and still save $$! The airfare was THAT much less. Sometimes we can stay that first night free using rewards points.
Another option for split stays- spend the last day super deluxe. It can be a 'budget' way to get the most out of a deluxe resort room view- or to take advantage of certain amenities- if it's not going to be a park day/rope drop day.
We've also done split stays where we drove to WDW. Spent one afternoon/night at the beach/recovering from the drive, then drove the next morning to WDW. It worked very well, but again we didn't unpack- just an overnight bag. If you stay at a place like Hampton Inn, which includes free breakfast, it's quite economical.
Oh - and let's not forget split stays to take advantage of the rest of Orlando. If you want to see almost anytign beyond the confines of WDW, a split offiste stay is a great way to go.