Now let's take a look at all the doors in the apartment. All of them should shut tightly and fit properly in the frame. There shouldn't be any problems with the doorknobs or any locks. Check to see if any paint is missing or mismatched as well. Also, make sure that you have two sets of keys to the apartment -- the front door should have a normal lock as well as a deadbolt you can secure from within.
In the bedrooms, check out all the closets and make sure the shelves aren't loose. If you haven't checked any of the above items in the bedrooms, now's the time to do so.