One that really bugs me is just after you kill your first dragon.

You're making your way back to Whiterun from the Western Watchtower and a guard says ''There's been talk among the guards that you're.. Dragonborn.. but such a thing, surely that is not possible?''

HOW THE HELL DO YOU KNOW WHEN YOU WERE NOT EVEN THERE AND NONE OF THE OTHER GUARDS HAVE MADE IT BACK YET!?