The floor is often the first thing you notice in an apartment. When moving in, make sure the carpets are cleaned and without snags or tears. Be certain that the carpeting is everywhere and no pieces are missing. The carpets should not be stained and should not smell bad, either.
For kitchens and bathrooms, check to see that the floors have been mopped and swept. Tiles should not be missing, scraped, scuffed or popping out.
When you're moving out, make sure the floors and carpets are clean and undamaged. Run the vacuum or steam clean if you have to. You may also want to invest in some stain remover.