I have definitely saved a lot of money by disregarding products that are displayed toward the front.
I always make sure to check items like my milk, yogurt and meat for expiration dates. I always pull them from the back to get the best shelf life.
Though, with many things, such as fruit and vegetables, I find you can get some really fantastic deals on items that need to move out the door. These items generally have a shelf life of 2-3 days. If you shop at night, just before the store closes, you can really save a lot of money on your perishables for the next few days.