What does "This contract is void if signed after....." mean?

My boyfriend and I have 2 months left on a 12 month lease that we signed last February, but it has been a nightmare the entire time we have been here! The ceiling leaked for about the first six months that we lived here, flooding the entire bathroom everyday, until they finally got around to fixing it. Now there is still mold (which my boyfriend is highly allergic to) growing on the bathroom ceiling that they said that they were going to replace months ago. We also have not been able to use hot water in our washer since we have been here, found out that the fire extinguisher that we were furnished was not charged (that was almost a disaster), and have had bedbugs for months even though we throw out all our furniture and sprayed several times. We are very concerned for our health and the health of our three kids, and just want to be done with this place already, but we can't afford to pay for this place and a new place for the next two months. So, today, my boyfriend and I went to the office to ask the manager if we could just get out of the last month of the lease (January), but she would have none of it. She told us that the workorders that we had placed were not enough doentation, and that legally she could not let us out of the lease even if she wanted to. Then, she just condescendingly insisted that we should read our lease again. So, when I got home that's exactly what I did, and I noticed that at the very top of the lease it says "This contract is void if signed after January 1 2010." What does this mean? And, is there any way we could us this to our advantage?