A little background about why i love HP-Fanfiction (and of course why i loathe some of the stories).
The reason why i love them is simple: you (the unknown author) can change everything.
Reading something different thats what i seek, cause after the xx-time reading about the
same drivel it's no fun anymore.

J.K.R.'s world could be fantastic. Everything is there, waiting for some good stories.
Her stories are the foundation. Sadly they are written for children.
That's not bad. But she makes it soooo hard to believe in them.
Want some examples? Let's talk about names...never ever let her name someone.
Sprout, Flitwick, Quirrel...and the best: Remus Lupin (with such a name it's no wonder
he is a werewolf).
A bank run by Goblins? The same creatures that battles against magical humans owns
all the gold? Sounds like the americans give the russians all their money.
The evil one...funny that he strikes only at the end of each year.
4th year, who would stop the fake teacher from kidnapping Harry at the start?
If Voldy can hide himself why not Harry? Why making stupid plans with unlimited
unknown factors and hope that Harry wins the tournament?
The children always in the middle of an adventure and the adaults don't know anything?
No wonder there are so many stories with Dumbledore manipulating everyone.

That said, i still love FF.
If at last they are a little bit logical...and are somewhat different from the main plot.

I hate stories with:

Harry gaining unknown powers without reason (hey, he just turned 16, now he can cast
like a pro).

Him getting more money than possible. Have those authors ever thought about how
the Potters could get the money? I mean investing in the magical world is out...every
store is owned by a family, the Gobblins don't give interest. The magical world is very small.
And the prices are low...a wand, something you would buy only once costs 7G?
So stories with him as a billionaire are only possible if his ancestors were high in muggle robbing.

An unknown person just jumps out of nowhere. Never heard of him/her before. And has
big powers. Again ask yourself: why has that person never done anything before?

Any pairing. ANY!!!
They are children, teens. How many of your old school buddies have married each other?
For teens ever lasting love is around 3 - 6 months.
And there are no such things as bonding. What are the chances that you would find your
one and only true love with 7 billion people worldwide?
And the usual suspects are just ...eeeekkk.
Yes, some of my fav stories have those pairings..but only because the author makes some
big changes...and i still don't like them.
Why? What do you seek in someone you love?
Compatibility.
And face it, even with 8-9 months school together they know nothing about the other person.