This one is easy for me, as I have had 20 months away from living with the RAH, and our divorce was final last week, so he is now truly no longer part of my life.
I want a relationship with someone that includes mutual respect and consideration. Similar (note I do NOT say same) goals and values. Similar priorities. Someone who is emotionally mature and self aware. And someone who enjoys life, regardless of what is happening in it. Must have patience with teenage girls and rowdy puppies. ; )
I could get more specific, but those are really the core things I seek in a companion.
Emotionally mature and self aware is a biggie. Someone who has incorporated these abilities has the flexibility to roll with life's punches without completely falling apart or turning to drugs/alcohol as a salve to wounds.
I suggest you think more in the abstract instead of focusing on the small details of things you don't like right now. So what if he quits drinking, stops looking at porn, and starts attending functions with you and his child? What then?