Get some houseplants. Seriously.
They not only clean the air but they help humidify it, too. Here's a cool article:
Best Air-Filtering House Plants According to NASA! : TreeHugger
If that link doesn't work - google "NASA houseplants"
It's also nice - when the weather cools down - to keep a simmering pot going on the stove with some things in it like star anise, cinnamon sticks, orange peels, cloves, bay leaf, a few drops of organic essential oil, etc. Adds moisture to the air plus it smells awesome!
Also - I'd recommend cleaning your carpet again with hot water and vinegar like someone else recommended. We've lived in quite a few rentals and what happens is that the cleaning companies that clean often use a lot of chemicals or soaps and things when they clean the carpet and a lot of residue is left. Or rent a steam cleaner and clean it with just steam. I hate carpet. We've had so many problems with carpet.
Good luck!!