Charging 12V Battery from AC-DC Converter
I think batteries usually follow a CC/CV or constant current/constant voltage system to charge up batteries. The LiPoly batteries need such a mechanism. So, this can be achieved by a system that sends out PWMs that control the current and voltage in a more controlled manner. Ofcourse lead acid charging will be different. But please read up on that as I believe you are bypassing that. 

And yes over-charging is definetily an issue in your case. You can ofcourse have a dedicated IC or even a combination of op-amp/comparators to do the job for you. When the voltage in the battery reaches a specific value then have the comparator/opamp circuitry turn off or isolate it via a MOSFET(again check the current rating and heat dissipation here).

What you are doing is blindly charging the battery which can very well end up in a pile of ash.