Last May we moved into a 2 bedroom apartment and things began going downhill from day 1. When we signed the lease and security deposit form our landlord gave us the letter he sent to the utility company stating when we will be moving into our new place. At one part is said "they are moving out of the hell-hole...." referring to the building we currently lived in. I found that very unprofessional. The morning after we moved in our toilet overflowed. We left messages with the landlord and maintenance and did not get a call back. When we still didn't a few hours later we called the back-up maintenance guy and he just said "what do you want me to do about it?" This happened several times in the 10 months we lived in the apt. I am very sensitive to cigarette smoke and was having difficulty in the first few weeks after we moved in. My fiancée and I both noticed that our socks or bare feet would be black by the end of the day. So we rented a carpet cleaner and cleaned the carpet. The water needed to be emptied several times and was black! It was terrible, I have never seen carpet that bad. We were told that the carpet was shampooed before we moved in, however, the stains that were in the carpet came out when we did it ourselves.
There are several other issues including a dryer that did not work well and we would get hung up on if we called about it. One day there was a smoke smell coming from the laundry room and my fiancée called about it. The landlord just said, "Well it's after 5 so I don't know why you expect me to do anything about it today." We were just trying to let him know, smelling smoke is not a good thing. We also went almost 2 months with almost no hot water... during the winter! When people in our building complained enough the water heaters were finally replaced, but this did not solve the problem... after non of our phone calls were returned my fiancée finally went to the office about it. The landlord sent his maintenance guy over to check. It turns out only one of the two water heaters was lit. This was 2 or 3 weeks after they were installed!
We have recently moved but were told we cannot get out security deposit back "no-whining!" is what is stated on the deposit form. Again, very unprofessional. If there is no chance, I guess I will have to live with that, but I would like to know who I can talk to about the situation. I don't think it's right for a person to run their "business" this way and take advantage of people.

Small Claims Court based on the facts, not the "right" and "wrong." Sounds like an awful situation, unprofessional landlord - so take the facts and proof to Court and file.

Depending on the hot water situation ("almost" no hot water may not qualify) you probably should have gone to housing court - if the apartment had been found unlivable or marginal you would not have to have paid rent for those uncorrected months.

As a landlord I am astonished by the "no whining" clause -

How can I prove some of these things, I'm not really sure where to start?

You call in a Housing Inspector, he/she makes a report, you use that as your basis to sue.