I have it too....a white exclamation mark on a blue ground. Perhaps it's always been there, I don't know. I checked all the categories in About Phone....no apparent problems, except that I do have some idle apps....wonder if it's that?
I'm thinking that the smartphone icon with a blue exclamation mark is just the icon that Android or LG chose for "About Phone", and that the exclamation mark itself doesn't indicate a problem.
I don't have anything to back that up, just my thought.
Edit/Update: The two G2's I am looking at also have an exclamation mark on the smartphone icon for About Device; so probably an LG icon (and not Android as surmised).
If the icon remains the way it is, I'm willing to bet it's just Google's icon for "About phone". A lowercase "i" with a blue background (circle) typically means "Info"
I don't think any of the icons in the settings menu are live icons, so nothing to be concerned with. Perhaps an update changed it, if it wasn't there at one point. Maybe a carrier specific icon, if not preset on all models.