j.k rowling's mistakes

did you ever thought that rowling has done mistakes in the series

for instance, in the sixth book(half-blood prince).the mistakes in half-blood prince book are as follows:-

1. draco hitted harry with a spell when he was under the deathly hallow cloak of invisibility which couldn't be hit by a spell!
2. dumbledore's wand wasn't snapped in two and according to a wizarding custom a wizard's wand should be snapped in two and layed with him the custom was introduced after the burial of aragog in a poem sung by hagrid and slughorn-"And Odo the hero, they bore him back home
   To the place that he'd known as a lad,
   They laid him to rest with his hat inside out
   And his wand snapped in two, which was sad"

it all ends on 7.15 because neither can live while the other survives and one is gonna leave for good.who is it gonna be?the boy who lived who is shown killed by or the boy who killed?will the survive after harry threw himself and dark lord off the cliff?? will harry crawl intime to lay his hands on the strongest wand of all times??