Someone really smart (I don't remember who) said fanfiction was like sex. As long as you did it in your home it was okay because once it got into public it was a taboo subject. Or something like that.
But anyway, I find it very true. Only a few people IRL (In Real Life) know that I write fanfiction, and they tend to think nothing of it. At least I think so. I'm not really sure, it's not something that people really talk about.
Things To Look For in Fanfiction
Mary Sues
Not necessarily a bad thing. Mary Sues can work, if they're done well. Others, well...just suck. They have no faults practically and have only one purpose: to fulfill the author's wishes in that fandom. Most make for an unrealistic story and a bad story at that. More links: Self Insertations and Mary Sues Mary Sue and How to Avoid Her Mary Sues
How to Write a GOOD Mary Sue (This deals with Ronin warriors, but can be revamped to almost any fandom.)
Cliches
The same plot OVER and OVER and OVER. Happens in every fandom. Chances are that your very first fic in every fandom will be a sort of a cliche or Mary Sue-ish. Don't worry, they usually make allowances for those undeveloped. Very boring, very ordinary...and very bad to read.
Ways to avoid writing a cliched fic:
Note the difference between INSPIRED and PLAIGARISM. If you've read a story and it inspires you to write, make sure that you aren't recycling that author's story. It tends to piss the author off, and that isn't good.
Put different twists in the plots. Spice it up a little. Do something that you've never seen done before!
Co-write with an author. I co-write with my friend Morgan *waves to Morgan* and you would not BELIEVE some of the stuff that we come up with.
But, aside from these difficulties, you can get over the hurdles just fine with practice and write one helluva fic! What are you waiting for? Break out the pens, pencils, and notebooks! You've got stories to write!