I have already extolled the advantages of the meat section's clearance area. Buy meat on the last day before it expires and get 50% off in most cases. If you aren't cooking it that day, put it in the freezer. It's a hit-or-miss proposition, so I freeze things I find if it looks like I will ever use them. When I gave the freezer its annual defrosting last week (way less traumatizing than last year), I went to the store early and loaded up on 75% off items that I don't normally buy, like ground veal.
The dairy case sometimes has a 25% sticker on items that are about to expire, usually yogurt. Since you can't freeze dairy for later, it has to be something you need that day.
Lately, I've seen some produce on clearance. It's usually older bananas that have been taped together with a sticker giving the price of a bunch. It would be great if they did that with pears. Or maybe the market has small apples or potatoes that are bagged at a single price.
The baked goods section is always slapping discount stickers on day-olds. You just have to get there early.
Then there's the non-perishable clearance rack. It is often hidden in the back, next to an employee door. All sorts of peculiar items end up there. Dented cans and partly crushed boxes are the most common items, but you can also find perfectly normal things that are not even close to the end of their shelf life. Perhaps the market lost its contract with the vendor and needs to clear the stock, or the item has been discontinued, or it's something seasonal like Christmas-themed hot chocolate. One time, there were several dozen jars of baby food that had nothing wrong with them. Last week was a Japanese food bonanza, with two brands of Panko bread crumbs, wasabi tins, and tempura batter mix. One time, I found a jar of saffron discounted to $1.99, by someone who obviously had no idea how expensive saffron is. Depending on the market, the items will be marked either with a %-off sticker or a new discounted price.
Again, you're not saving money if you never use the items. But if there's something on clearance that you do use, it's perfectly safe to buy, cook, and eat it. Just use common sense and you might get to try some new ingredients you have never used before.