Saving (and bottle carbing) an infected batch

I had an amber ale extract kit sitting around that I got from a friend. I had some time and ended up using it a while back, and probably not paying too much attention to sanitation. I took a peek a while ago and had a thin pelicle on it, though I'm not sure what exactly it was. I figured I would go ahead and prime and bottle as usual, making sure I used a plastic bottle so I can check carbonation as it goes. I planned to pasteurize the glass bottles as soon as the plastic one seemed carbed. That was three days ago and I just put the plastic bottle in the fridge last night since it was rock hard. This morning I released the bottle cap rocket and it was fully carbed up. It tasted alright, though a little thin, nothing I would have a problem drinking most days. The question is, has anyone ever had something carb up that quickly? How soon should I get to pasteurizing the other bottles?