I updated from iOS 8.0 to iOS 8.0.2 on my iPhone 6 last night and noticed after the update completed that the Settings app shows a badge on my home screen even though there is no apparent update available in the app (including an iOS software update – which shows iOS 8.0.2 is installed and is the latest version).
I saw a comment elsewhere (ios 8.0.1 – download completed but unable to install) implying this was seen with iOS 8.0.1 also and wondered if there is a way to reset the settings app badge or if this may be a bug that remains in iOS 8.0.2.
UPDATE: As an additional data point the count on the settings badge inexplicably went from 1 to 5 today. I have not done a DFU restore, and may eventually resort to that, but for now would rather not go through that process and am hopeful a different fix is possible.
Best Answer
I found a MacRumors thread complaining about the same thing, and more Google results about the same problem happening as far back as iOS 6. It can apparently be fixed by a DFU restore, if you're willing to be that drastic. Otherwise...wait for the next update.