I've actually learned something from putting this "eye" thing on the blog. The way I tell damselflies from dragonflies is the way they hold their wings when at rest. The dragonfly holds them straight out from it's body and the damselfly folds them back. However, there are other ways and one of them is the eyes. The damselfly eyes are as far apart as they can be on the head - located like a hammerhead shark's. The dragonflies eyes are located so close together they look like they touch.
Something you can casually mention the next time you want to make small talk with an entomologist.