Well, this is a good question, since I used to get confused about it. However, actually, our eyes would not be damaged by looking at the moon. Why? Since moonlight is far less powerful than sun beams, which could even make your eyes blind! But, I believe you cannot be interested enough to look at it the whole night right? So, normal stare would do nothing harmful to your eyes.
Not really, the moon light is not so exactly as strong as sunshine. It is the reflection of sunshine. We are usually contact all the staff which reflect rays from sunshine. Most of the species are evolving into the one who would use to the reflection of sunshine. The creature who could not stand the reflection of sunshine, has already extincted for many years. The moonlight will give people gentle or soft feeling, especially in the eastern Middle Autumn day, we like to watch the moon which symbolized the reunion of whole family. No body being hurt for thousands of years. No worries. Enjoy your time with romantic moonlight.
Yes, you are right; it can not be harmful for your eyes, when you stare at the moon. As we know that the mood is not a source of light but reflects light from the sun. so staring at the moon is not bad for your eyes. But on the other hand, if you do stare at the sun, you can and will have harmful effects to your eyes, for the light rays from the sun are very powerful and cause a burn on your retina. In some cases, it also can lead to blindness. So just be careful about it.