I just got the second floor to the museum in New Leaf and I hung a bunch of designs on the wall and a few dresses standing up. I went to the able sisters to get some more qr posters online. I came back and the ones I'd replaced in my designs (which I have saved with mabel but I assumed I wouldn't need them any more for now) have all disappeared from the room. Does this mean you can only display designs that you have on your person? Because what's the point of being able to display your artwork if it's going to disappear if you want to have new designs? Otherwise the rooms are basically just going to be museum versions of your own house surely? Help?
Yes, you can only display designs in your town that are currently in the 10 active slots on one of your characters.
You can save designs via displaying them in the Able Sister's Shop and/or by talking to Mabel and asking her to save a design for you. However, if you move Design 1 in Slot 1 to Mabel's save, then put a Design 2 in Slot 1, Design 2 will be the one that shows up in the game. Design 1 will still be accessible, but will show up in-game only if you go back to Mabel and place it back in one of your active slots.
In order to get around this limitation, you can create other residents in your town and use them essentially as "design mules". Making a total of 3 other residents will give you another 30 active slots to play around with.
Otherwise, yes, you are correct, the other rooms can be essentially used as museum versions of your house (which won't be graded by the HHA, obviously). Given that you get special carpets for turning in X amount of Bugs, Fish, and Fossils, I'm personally going to be using those rooms to display extras of those things that I think look neat. I'm also making a Nintendo room. It's mostly extra space to give you opportunities to show off your collections.