I work for a company that manages and develops apartments, and I want to caution you against withholding rent at this stage. In most states, a tenant may only do so legally if he or she first notifies the landlord of the problem in writing, and gives the landlord an opportunity to correct the problem. Then rent can only be legally withheld if the problem is a violation of code, and in some cases the rent would be held in escrow.
There have been many high profile cases in the housing industry involving toxic mold. To make a distinction, not all mold is toxic, so there may or many not be a hazard. Just don't want to worry you too much!
Sometimes it's very hard to remove evidence of all prior residents from an apartment. Heavy smoke and cooking odors are the worst. Even if the carpet has been changed, they may have left the carpet pad, or the odors may have permeated the concrete flooring below.
Do let your landlord know about this ASAP. If the company is conscientious, they'll do everything possible to fix the problem and take good care of you, as well as their building.
Good luck!
