Well, I think we can safely say that the sorting hat was wrong, 3 times.. 1st time it was wrong was putting Snape into Slytherin. Clearly, he should have been in Griffindor because of his bravery. Sure, he was a dark and loved the wrong things, but he was also brave and a mud-blood.. Slytherin wouldn't have wanted him in his house. 2nd time, was Voldemort. Again, a mud-blood. Shouldn't have been in Slytherin at all, regardless of who's blood he had. 3rd time was when the hat told Harry that it'd never been wrong before.
You meant to say Half bloods, right? Mudbloods are all muggle borns.
First Voldemort, because he wasnt pure blood. But his one side wizard blood was very strong to Slytherin.
What is the ultimate sign of being a Slytherin? Clever and cunning. Can you find a more clever and cunning Slytherin than Voldemort?
So, can we really say sorting hat was wrong? umm... no, not in my opinion.
Snape was great to die, and aid Harry in the end.
But originally he wasnt. In early life, he was as dark as they come. He fancied dark arts and ended up being a death eater.
He probably would have stayed as a death eater, if it wasnt for his fiasco and Lily's death, who was the only person he loved in his life.
So sorting hat is right in that decision too.
Harry showed up with a part of Voldemort's soul in him, that is why Sorting Hat took long time and kept wanting to put Harry in Slytherin. It was Harry who wanted to belong to brave.
So in my opinion, Sorting hat wasnt wrong there either. It was hoodwinked by accidental horcrux in Harry.
I think DD's statement about sorting too soon, was more like a sarcasm towards Snape, than a fact statement.