On a month-by-month, you don't ned to give a reason to vacate. So just put your notice in in writing and that should be it.
I'm glad you took the photos when you moved in. I reckon if your LL hasn't done repairs, they will try to pin it on you. Some LL are bad like that and it sounds like your Agent isn't that great either.
If you run in to problems, feel free to PM me. I may not get back to you quickly next week, but I will be around