If you're at the grocery store, look for broccoli that is firm to the touch. You also want to make sure the florets are dark green and tightly closed. If you see any yellowing, you want to leave that broccoli behind. You want the stems of the broccoli to be thin too. Thick stems indicate that the broccoli is old. Another indication of old broccoli is any flowers. You're more likely to see this on broccoli you find at a farm or farmer's market than at a grocery store, but it's something to look for.