I bought a carbon steel paella pan. I've looked up if people season it (link) but on Wikipedia I've read:     As with other cast iron vessels, a seasoned pan or dutch oven should not regularly be used to cook foods containing tomatoes, vinegar or other acidic ingredients, as these foods will eventually remove the protective layer created during the seasoning process.   I think paella is pretty acidic food, so is it a good idea to season the pan? 
They're meat spots, and safe (though unpleasant) to eat. 