I left milk out in a jug, bought brand new, for twelve hours. Is it still safe to drink?
Dairy is something of a special case because the natural bacteria in dairy products will tend to outcompete any interlopers...In short you're more likely to end up with a kind of redneck buttermilk (from the action of natural Lactococcus lactis or Lactobacillus bulgaricus) than something that is toxic to you. So unless the milk was already contaminated with something not normally native to dairy, you should be fine. The taste will likely have gone substantially off though.
Note: we are assuming that the milk was pasteurized. Raw milk is prone to contamination with things like listeria and e. coli, and those would certainly cause you some upset.
I would...with milk you generally can tell the moment it comes near your nose or touches your tongue whether it's gone bad or not.
That doesn't mean I would serve it to others, that's risking someone else's health.