I know that I have some contacts that have a glowing dot (green on stock, blue on my rom) for when that person is online on google talk, so it may have something to do with that, I'm not sure.
next time it happens hold down the home button and the power button at the same time to take a screen shot so we have a better idea of what you're seeing.
It is the google talk status for that person. You may not use google talk but you are currently signed in. Go into google talk and set it to not auto sign in when you start the device and then sign out. The circle with an x will go away.