Know Your Canon. Screencaps and scripts are your bestest best friends. Use them. A lot.
As an addendum to that--Know Your Characters. If you've got pre-soul Angelus giving a teddy bear to Spike, who subsequently carries it everywhere because he loves it so much, you've got a problem. And yes, that goes for post-soul Angel as well. River creeps Jayne the hell out; if you want them to get together, you'll have to deal with this issue. That being said, if you can sell the characters doing something that they wouldn't normally do, more power to you. But sell it. Don't try to shortcut characterization by saying "He started looking at her in a new way" and leaving it at that.
Grammar and Spelling Are Important. No, really. Netspeak and Leetspeak make you look very very stupid and will get you GAFFed and FanFicRanted. Just say no to "r" and "u."
The Dreaded Mary Sue/Gary Stu. If your Original Female Character is eclipsing the canon characters, making them act OOC, making the boys fall all over themselves to worship her, and warping the story so it's all about her? Scale her back. Way back. If your Original Male Character is a better fighter than Methos, smarter than Giles, a stronger wizard than Gandalf, and the most handsome guy in the room? Stu alert. And be careful about turning the canon characters into Sues or Stus (Xander writers, I'm looking right at you). Good characters have flaws, and you can use them to all sorts of interesting advantage. Perfect characters = boring characters.
As an addendum to the Dreaded Mary Sue, bamfing yourself into your fandom of choice is generally a bad idea. Self-inserts are rarely well done, even when they're not as blatent as "I fall into Middle earth and hook up with Legolas!"
That being said: Write the Sue. Embrace the Sue. Everyone does it, at least once. The first fic is like the first pancake; it's for the dogs. But if you don't write the first fic, then you can't write the second one. Get the Sue out of your system and make your favorite character happy. Then you can write the awesome stuff that you're capable of without having that hanging over your head.
Songfic. If your fic has more song than fic, or if it doesn't make sense without the lyrics? Retool it. A character sitting around listening to Evanescence and emoting all over the place about the song is dull as dirt. Also, fanfic skates at the edge of legality as it is. Putting song lyrics in there that you didn't write? Bad idea. And if you must write songfic, make sure your characters are listening to music of their own era. James and Lily Potter aren't going to know who Nirvana is. Or what a CD is, for that matter.
Get a Beta Reader. Just make sure that they have a grasp on your chosen canon, or that they have other skills you can take advantage of. Also? Their word isn't gospel. You're allowed to pick and choose which suggestions you take.
Random Humor Isn't Funny. No, really. Sugar-high crackfic with characters running into walls and screaming "Cheese!" at each other is stupid, not funny. Monty Python can get away with it. You? Not so much. Because if you can, then what are you doing writing fanfic?
The Sex Scene. Bad euphemisms only make people giggle. "Molten core" is a no-no. "Weeping cock" is just as bad. "He put his sex in her sex and they had sex"? Yes, that's an actual example, and really, you should just fade to black if you're going to write that.
POV Shifts. Pick a POV for the scene and stick with it. A reaction shot as the POV character walks out of the room can be used to good effect, but don't give your readers whiplash by putting them in three different characters' heads within three paragraphs.
Character Bashing. We all have characters we don't like. But if you have to write them Out of Character to show your extreme hatred, then you're not writing that character, you're writing a pod-person. Riley isn't a rapist. Kate isn't an emo whiner. If you must villainize a character, at least turn them into an interesting villain.
Do Not Use Rape as a Plot Device to Get Your OTP Together. This is a Bad Idea. The Healing Cock does not exist in real life.
Crossovers Can Be Fun! However, an attempt to make them plausible is always appreciated. Portals and wormholes, while overused to the point of cliche, are handy tools. If they're already part of one of your chosen fandoms, all the better.
Feedback Is Important. Feed the authors. Reviews are the only payment we get. If something in a story particularly touched you, if a certain line made you laugh, pull a quote and let the author know. Constructive criticism isn't always welcome (some people are horrid brats about it, in fact), but if an author says they want it, then by all means tell them what didn't work for you in the story as well as what did. By the same token, if someone leaves you less-than-flattering feedback, receive it with grace and see if perhaps the reviewer has a point. If all you ever get is slobbering praise, how are you going to get better?