It looks like an "eye" and appears at random infrequent intervals and disappears before I have a chance to figure out what it is. Any comments?
That's SmartStay. When activated (yours obviously is) the front camera looks at your eyes at regular (30 sec?) intervals. As long as you're looking at the screen it won't turn off.
I think it's an awesome feature - but you can always disable it if you want.
Phones: OG Droid >>Droid Bionic>>Moto X