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"