So we gave our apartment notice that my husband was being transferred and we would be moving. Since then, they have said they are charging us a 75$ fee for pet waste (which we were out of state when our dogs supposedly did their business) they informed us of a ware bill due the 12th and there would be a late fee of 100 dollars if not paid in 2 hours. We have had other issues with them including losing our deposit, a pipe breaking in our living room the first day we moved in, and mold in our closets, as well as cockroaches. My question is whether it is legal for them to be able to charge the water bill and "fees" if our agreement says it is due on the 1st? I have an apt with legal, but curious as to what you guys think 

Before you pay anything ask him if you can look at the agreement again. There may be a loop hole for him if you are leaving soon. What's sad that if you agree to it he can hold you to it. If you don't have evidence that it isn't your fault he can make you pay. But I would say look everything over in the agreement. You have the right to see it. If you are within your rights you can take him to court. 

IMO some things are worth fighting other things are not. Since it is your water bill why not just pay it and be done with them?

Honestly in the lease there probably is a clause that if you terminate lease you are to pay your final water bill at move out ( or something to that effect) but they can't charge you a $100 fee if that is not in writing in the lease. So, be sure to read over your lease very carefully.

I do know that there is a way to put $ in escrow accounts if a tenant has an issue with landlord, but I don't know the provisions. 

Everything says it is due the 1st, late on the 4th. I don't think having a bill show up in the middle of the month should count as late given those provisions. The issue was that I pay my bills by check or cash/cashiers check only (they had a huge breach of their site an people's identities were stolen, so I refuse to pay anything online). I have no issue with paying it, but I'm one of those people that will fight just for the principle of the matter. She "waived" our pet fee seeing a our dogs were out of state with us.
And the situation was that my SO was getting moved to another unit for medical reasons, so we gave them notice that as soon as they put the final touches on his orders, we'd be moving. My point is that our lease says that water and rent are due on the 1st late on the 4th, but I don't think it should be late if they presented it in the middle of the month. Again, I paid the bill, but have much better things I can do with 100 dollars...