I worked in Property Management in California for over 3 years, and rented in several states. The laws about when,how and why a landlord can enter the rental premises vary from state to state and you should check with your local government housing agency for complete details.
In general, yes, they can enter to see if the unit is clean. Your contract more than likely has a clause that states you as the renter are agreeing to "keep the unit clean, sanitary and free of an objectionable odors". So, therefore, yes they can check to see if you are upholding your end of the agreement. However in most states they must gain your permission to enter the premises or serve you a 24 or 48 hour notice to enter. Also, common in most states, they can only enter Monday through Friday during normal business hours!