Rule #1: Control indoor pollutants. Minimizing what is brought into a home -- especially into those tight apartment spaces -- is just about the leading recommendation for addressing air quality of almost every expert we've encountered.
Rule #2: Don't smoke. Duh.
Rule #3: Limit your intentional use of pollutants. For example, you can try cleaning with less-toxic substances. Baking soda and vinegar is often recommended by back-to-nature types as a home-cleaning scrub, replacing industrial-strength cleaning solvents.
Rule #4: Ventilate, ventilate, ventilate. To mitigate the effects of indoor pollutants, consider more venting. The more "bad" stuff you can direct outdoors, the better off you will be. This may be harder to pull off if you rent, but if you can afford it, there are numerous models of outside venting exhaust fans you can install in bathrooms, kitchens, and laundry areas that will help rid you of the organic pollution that emanates from the hot water used in those rooms.
If that's too big a deal, vent the old-fashioned way -- open windows and doors -- when you're doing your industrial-strength apartment cleaning and when you're using air freshener, hair spray, or nail polish.
Rule #5: Take good care of the a/c. Whether it's central, through the wall, or in the window, at a minimum follow the recommended maintenance procedures (one of those things no one does, but if you saw an analysis of what's in the equipment that hasn't been cleaned, you'd be afraid to take in another breath).