There are other ways to save at the grocery store beyond coupons. One of the best ways to save money is watch your prices. Watch them figuratively by shopping around for the best deals and stacking them with coupons, but also watch them literally when they are rung up at the cash register. If a scanned price is different from the price marked on the shelf, you may get that item for a discount or even free.
Mass merchandisers, grocery stores, and other chains nearly always have scanner policies that compensate you if a price scans incorrectly — either too high or too low. In many jurisdictions, laws require stores to give you the item for free or the price difference plus a bonus if the scanner price is too high. Some stores expand their policies to include prices that scan too low because it benefits them if you catch their mistakes.
If you have trouble following the prices while they are being scanned at cash register, consider taking along a calculator to keep track of what your total bill should be. If the total at the register is off, you'll know to look for errors. You might also devise your own system for remembering the prices of the things in your cart.
Be sure to take the time to check your receipt before you leave the store. If any prices are incorrect, go back immediately to the cashier or to the customer service desk and ask about the store's scanner policy. At the very least, they should correct their mistake. Checking the receipt also ensures that you haven't paid for items you didn't buy, which sometimes happens with large orders at grocery stores. Once you leave the store and have the merchandise home, you can no longer prove that you never bought those items. Having your full shopping cart with all the items right then and there helps your case.
Some bargain hunters make a game of finding scanning errors. Whether or not it's something you enjoy doing, watching prices as they scan is a good way to ensure you aren't overcharged, and you may earn the surprise benefit of getting something you want for free.