If there is a furnace, make sure that there is a new filter in the ducts. Do they have kids? Call CPS. Do they have pets? Call Animal Control. And call HUD before they come and tell them to inspect. HUD lends money for repairs at VERY low rates, they don't need the apartment to be trashed. Where is the landlord in this?
Here's a little story about how we got the down payment on our first house. We were living in low-income housing and the owner got HUD loans at .5% to make repairs, which he actually used to build new luxury homes and sell when the market was hot. He never made any repairs or did any upkeep for us. You can use the Freedom of Information Act to access all HUD condition reports and loans, which we did. We had a black mold problem which he refused to fix. All we had asked was for him to paint with a mildewcide. He wouldn't do it.
We withheld rent with notice to him that we would not pay rent until the black mold was taken care of. We set the rent aside in case we didn't win this little battle. This was about October. He went to court and tried to evict us. I was aware that the HUD inspection was due in January, and I brought up all property issues. Problems with the laundry room, feral cats, other neighbors' rotting floors - everything. The judge found in our favor that we did not have to pay rent until a HUD inspection showed that he had repaired our problems along with problems in all common areas.
January and the inspection came, and he had painted our apartment. Period. The HUD report came, and it listed all sorts of problems that he was to fix within 60 days. The re-inspection showed that all he did was paint our apartment. We did not pay rent ever again. When the next year's inspection report came and he still had not fixed anything, we told him that we would move if he gave us a year's rent, which he could then collect from the next tenant. He did not agree to that, and we continued to pay no rent. We then started looking for a house, and had our down-payment.
Everyone in the apartment complex hated us. There was a non-disclosure agreement, so they could only suspect what the truth of our agreement was. Who cares? I looked him up once Google became easy to use, and he was also fined $12,000 by HUD for taking loans and not using them for their intended purpose, and he lost property for not paying property taxes. Boo-hoo.
I'd strongly recommend that you coordinate with HUD on their inspection. They're more than happy to help a tenant suffering due to a landlord's negligence.