As a fanfiction writer myself, I try to give it a good name. I will say that there is a lot of it out there that is truly horrible, but I have yet to find one that completely destroys me.
Personally, I hold high standards for my own stories, and low standards for other people's stories. The high standards I put on myself let me write the best stories I can, and having low standards for other people's stories lets me enjoy even a mediocre fanfic.
It's a mixed bag really. For every person that carefully writes, carefully plans, and carefully proofreads, there's about ten people that write the first thing that comes to mind with no regards for grammar.
A little tip: I stay far the hell away from fanfiction.com. Unless someone links to a good story on there, I stay as far away as possible. Seriously, there's some horrible stuff there. I stick to DeviantART, where people at least have half a mind. (Mostly).