Q: Red alert shown on setting icon

Did you check in the settings if another update is available or does the alert lead to another app that needs your attention?

Did you already reset the phone by holding the sleep and home button for about 10sec, until the Apple logo comes back again?

Did you use iTunes to update or did you use the build in software update "Over The Air" feature?

If you are running 8.0.2 now, the badge should be gone, if there is no other action to be taken in the settings.

It could be a carrier update.  Those would show up in settings as well.

iOS: Updating your carrier settings