"How old is too old?"
That quite subjective. If it is flakes that you are talking about, since they are pretty cheap, it wouldn't break the bank to replace them with fresh food.
On the flip side, you can never tell how long the fish food has been on the shelves at your LFS
I vary my fishes diet. Flakes, frozen blood worms, flakes, frozen brine shrimp, color pellets, blanched zuchini (once a month or so). If they don't like the stale flakes, they can wait until tomorrow.