When people move, the normal tendency is to focus on the moving out - the things you are going to bring along, as well as the new place you will be moving into. Sadly, the place you are moving out of is usually neglected or lies low on the list of the priorities of the movers. Thus, many people get surprised when they don't get their deposit back, or worse, are billed with a statement for cleaning and repair fees.
 
In the same way that you inspect your new place, you also need to make sure that the premises you are moving out of is left the way it was when you first moved in, if not better. Just imagine yourself moving into a house or apartment improperly vacated by the previous occupant. It is simple courtesy to ensure that you leave the place clean and orderly before moving on to your new place of residence.
 
Another thing to consider when moving out is to settle all outstanding bills so that when you get to your new place, you start with a clean slate. Also make sure to inform all concerned that you will be changing your residence and address so that any important mail that is sent to your old address will instead be forwarded to your new one.