J.N.
I can appreciate what you're dealing with. My husband travels a lot for work and we have two boys, 4 years and 18 months old. I seem to spend all my time following them around undoing the things they do!
I have two suggestions, one borrowed from my sister the army wife: she doesn't use ANY dishes or kitchen utensils that can't go in the dishwasher. She says, "if it doesn't go in the dishwasher, it doesn't belong in my house." She was even known to dishwash small toys when my nephew was a baby.
The other is get yourself some foldable storage cubes (the fabric kind that "pop-up" with a shake). They're great for tossing toys, clothes, etc in when you need to do a quick sweep though the apartment, and on the rare occasions when everything is in its proper place, they fold flat and can be stored under the bed (or sofa, or wherever you have spare room).
Good luck!
Jenn