Three common approaches to this:
1) call your local (city or county as applicable, depending on whether in an official "town" or "city" or not) health department, or if in larger city housing and rent control office - they will send an inspector, document the situation, and as loing as not directly caused by your actions (like pot growing, excessive house plants, constant running of humidifier, etc) issue a notice of violation to the building owners to remedy the situation - tuypically for things like this they have 30 days to start work and about 60-90 to finish remedial measures, which would be fixing the leaks, removing mildewy/moldy finishes and walls, and repainting/reflooring as necessary. If you can't find applicable department call the city/county health inspector's office, or the mayor's office for direction to the correct department.
2) if that does not work, or you want to get nasty, contact a lawyer specializing in housing and renter rights actions (or if disabled/poor maybe your local Legal Aid office - either non-profit or in some larger cities the city or district attorney's office offers legal aid services) and have the attorney write a letter threatening legal action, quoting the applicable regulations, etc. - followed up by suit if needed.
3) move out, preferably after having health inspector examine and document the conditions, and refuse to pay any remaining lease payments and demand your full deposit back because of uninhabitable conditions. Would probably be best to have official health department notice issued and/or attorney's input on documentation before doing this to be on the safe side regarding skipping out on your lease (assuming this is a lease situation). IF unit is owned by you, tougher by far because you have to not onluy prove the damage but also prove it is from something the building management is responsible for fixing, not you or other unit owners.
The first action is likely to get results, but runs the risk of the building being condemned till fixed, which can put all the renters out on the streets. The second does not carry the weight of government behind it, but does carry more chance of damages recovery. In both cases, depending on legal pressure and on local/state law, you may have a right of refund for rent for the period from your first notification to the owners to when the problem is fully remedied in your unit. Third option gets you out of there so solves the health problem faster - may or may not come out made whole financially.