I can't find this problem anywhere via google. It's not solved by resetting the regulator (and I'll argue that it shouldn't be below), and doesn't seem to be related to this cooking.se question.
Of my last four propane tanks, I've had this problem with two: I turn off all (five) burners on my grill and (obviously) leave the tanks valve closed, but as soon as I screw the regulator onto the tank valve, there's a hissing sound of gas and the accompanying smell. This lasts a few seconds, then stops. Note that this is before any valves are open.
Then, as soon as I turn on the tank valve (still leaving the burners off), there's more gushing gas sound. This doesn't seem to stop, even if I let it go for a good few seconds (maybe thirty in total). I've used soapy water to track the source of this leak, and found it to come from the back of the tank valve — the side opposite the threads, which I gather is the pressure relief valve.
In each case, I've attached a different tank with no trouble, then tried the bad tanks again and had the problem. So I assume that this is not a problem with my equipment. Maybe it is, and only turns up with some tanks, but I doubt it. My main point of evidence is that the gas is actually exiting the propane tank valve itself, not my regulator, hoses, etc.
Last time, I just exchanged the tank and ate the loss of money because I was in a big hurry. But now I'm wondering, is this a known problem? Should the store I bought it from agree to just replace my tank for free? Is there some reason this might actually be a problem with my equipment?
EDIT: I took the tank back to where I got it, told them the problem, and they just replaced it for free, no hassle.