I've read that you have to be careful with seeds from the squash family, as accidental crosses can make the fruit of your plants quite toxic. Even seed companies have fallen victim to this problem, with people buying packets of seeds for courgette, squash etc. and then being quite ill after eating fruit from the plants. I'm not sure I'd want to risk eating produce from a plant grown from seeds that you've harvested from a supermarket/grocery store squash... although in most cases it would probably be fine.
