The father may have become nice, but he still hasn't helped out financially in any way, and hasn't offered to.
You know what happens to a parent that does that in Florida? Their driver's licence is supended. This State is HUGE on paying your child support, as it should be and should be that way in all States.
Im unsure of country/local laws about child support but according to this
Dead Link Removed it seems to be the same so hell, take him to court for child support! That way he legally responsible for his part financially of raising your son and I would tell the father that until he starts to pitch into the cost of raising your joint son then he has no rights to see him. Fatherhood is way more than just seeing the baby once in a while and holding him, its also financially contibuting to the cost of raising him.
I get that you dont want to deny your son his father but his father is an abuser. Whom says he wouldnt get angry one day at the baby and shake him or something horrible? I wouldnt trust it. But he also needs to pay you towards the raising him and not just see him when he wants and that's it. He has no legal visitation yet.
Also, Id fight in court for supervised visitation. Due to the abuse he put you through and if you cant gain it in or dont want to fight in court for that, Id hold off visitation until you can find someone you fully trust that you both know that will be the person there. Saftey for the baby first!
But honestly, I would tell him that he cant be a part of the baby's life until he contibutes
something consistantly financially towards raising the baby, even if its a lower amount than the court would force upon him (but must be consistant, not here and there) or/and if he doesnt tell him you are taking him to court for child support and until he pays it then he has no rights to see the baby
AND tell him that you do not want him around
you (which you have all rights to say) and that he cannot see him until you find a trusted 3rd party that you can trust the saftey of your baby with to take the baby to his father and
stay there to supervise the visitation until you are comfortable (which can be a long time which is completely ok) that he would not get angry at and abuse your child.
Keep in mind that most that shake a baby arent abusers but someone where anger & frustration "snapped" to that level.
Not sure all is educated about shaken baby syndrome so here is some information about it.
http://www.mayoclinic.org/diseases-conditions/shaken-baby-syndrome/basics/definition/con-20034461
Under Risk Factors is domestic abuse.
These are just things Id do. He is the father which means he is bound to support his child in everything your child needs & does (later in life like activities he may get involved in) until he is 18 and as a past abuser of yours also is bound to show you that he will not be of any threat to your baby.