to remove red dot from voicemail
to remove red dot from voicemail, in settings (1) turn on cellular data. (2) In settings scroll down to "general," Under "general" scroll down to bottom of drop down and click "reset." Under "reset" click "reset network settings." Your system will reset showing the apple logo. After system recycles, turn cellular data off ( if you don't won't to use cellular data. Reconnect your wi-fi. Red dot should be removed from phone icon.
iPod touch, iOS 5