I always sniff milk before using it. I've had it go bad before the date a few times, but I've also had it last well past it. No rhyme or reason as far as I can tell. You can definitely tell when it's gone bad.
That usually comes down to the milk having gotten too warm at some point. Milk is pretty temperature sensitive and if it gets above 40 for even an hour, it's gonna turn quickly.
I've noticed that ultra pasteurized milk and half and half products last WAY longer than others, and that's pretty much all I will buy now. I got tired of tossing half full containers of chunky half and half after only being open a couple days.
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