1: We get to see Eddard Stark's body. We get to see Katelyn's body. We get to see everybody's corpses along the way. So why are we so sure that the son who was King in the North is actually dead? they didn't show us the corpse.
2: Jon Snow's obviously Katelyn Stark's nephew-by-marriage: not her children's bastard half-brother, but their bastard cousin by way of her sister-in-law. Jon was begat by the king who kicks off in the beginning.
Any other thoughts or observations, please feel free to add 'em in comments. If you want to avoid spoilerage, don't read the comments here.