Not much more to add; it's easy to pick up furniture/doors/stuff while saving.
I can confirm this. If something is behind the save screen and the player clicks the save screen (such as to select a lot to save over), the game will also pick up anything that's behind where the player clicked. Also, if your lot uses the hotkey to spawn a door or staircase, then either the door or staircase will also spawn while naming the lot. Scrolling the screen so the cursor can't click anything while saving is what I recommend for now.