Put blankets on the floor when moving large furniture. This will make sure that you don't damage the floors during the move.
While this may seem like just another thing that’s added to your plate, get copies made of all of the keys before you move. In all of the chaos of the move it would be easy to misplace a key, and that is the last thing you want to deal with on your moving day.
While it is not required by law in some states, be sure to do an in person walk through with your landlord before moving out. This way you can address any issues on the spot.