I've been thinking about the things that I keep running across when I read fanfiction. Really, this is mostly just a running list I've had in my head for a while, but I felt like expanding on these things since I've got the time now.
1. Epithets
I can't begin to explain my deep-set loathing of epithets. They are utterly distracting and add absolutely nothing to the story. (Of course Draco is blond; that doesn't mean you should refer to him as "the blond" every third sentence.) I think the problem is that new writers come across them and think of them as a wonderful way to add variety to their writing, as opposed to simply writing the names or appropriate pronouns for characters. But this is wrong, wrong, WRONG. They may offer some variety, but at the high price of distracting and annoying your audience, and it is not worth it. The only times that epithets might be appropriate are when they are ways in which your narrative character would actually tend to think of another character in your story - for example, Harry thinking of Snape as "the greasy-haired git." As long as it adds a sense of connection, of getting inside the character's head, then it is acceptable, but only used sparingly and never just for the sake of not saying a name/pronoun repeatedly.
2. In-Scene Perspective Switches
First, let me say this: I hate third-person omniscient. For me, I enjoy stories in which you can't read characters from first glance; if you are inside the head of every character simultaneously, what plot can be effectively conceived? Thus, I prefer to keep to third-person limited, either to one character or a handful of characters. But if you are using multiple viewpoint characters, you have to be constantly aware of which one you are using at the moment. If you are shifting between characters every few paragraphs, you create a sense of discontinuity, and it makes any connection between your audience and your characters strained, if not impossible. If you switch every paragraph, then it reads like a transcribed role-playing game. And if you switch every other sentence, that's just plain chaotic. My point is this: if you have any sympathy for your readers at all, stick to one viewpoint character per scene.
3. Bad Dialogue
There are many ways to define bad dialogue, and differences crop up between pretty much everyone. For me, "bad dialogue" entails a lack of characterization. In other words, your character is just spewing out words to perhaps further the plot, but bear no reflection on the character himself. To have "good" dialogue, I think you need to keep in mind several things. First is your character's mindset and motives. How does he approach the world? How does he interpret different aspects of it? Why does he think and behave the way he does? Second is an attention to voice. Every character has his own particular way of speaking. Some people use very formal language, while others tend toward informal slang. Some will refer to people by their titles alone, and if they make an exception, they have a reason for that exception. Some people will ramble on an on, expounding on things that they really have no business blathering on about (i.e. Hagrid), but others will speak succinctly, saying only what must be said and nothing more (i.e. Snape). Dialogue therefore isn't so much an issue of what is being said, but how it is being said.
4. Skewed Emphasis on Physical Descriptions
There are only so many times I can handle reading about Harry's shocking, captivating, world-devouring, emerald-green orbs before I want to tear my eyes out. Authors want to emphasize the things that they feel are important, and I can appreciate this. However, sometimes they need to focus on what it is that is truly important for the story. I admit it, I have a huge problem with doing this myself, but that familiarity allows me to see clearly enough when others have this same problem. So your sheets are green silk and his hair is soft as down feather, his skin smooth as cream - but so what? These are such overused descriptions that they lose their impact, and simple metaphors will not cut it. His skin may be soft, but does he have ragged fingernails from biting them, or calluses from gripping his broom? Your bedding might be silk, but is the duvet folded at the foot, or are the sheets tangled or stained from the previous night, and are the pillows piled high and the head or scattered around the bed? The more your audience knows about what your characters see, the better they are able to connect and feel along with them.
5. Half-Baked Sense Memory
This is along the same vein as the previous point. I see plenty of simplistic emotional description, i.e. "he was angry/upset/thrilled" etc. And when it's a fleeting emotion, that's just fine. But if you want to convince your audience, you need to put forth a little more effort than that. If your character is angry, why not describe the sense of heat rising in his face? If he's upset, why not describe the dread roiling in his belly? And so on. It's great to tell your audience how your character feels, but if you can convey his feelings without needing to include the simplistic forms as a means of explanation, then it's all the better for you and for your audience.
6. Unexplained Changes to Canon
There is a difference between a point of reference plot twist and an utter bastardization of the canon. For example, if Harry hadn't been given a preconceived notion of Slytherin House, then a plot can be spun from him accepting the Sorting Hat placing him in that house. This is not the same thing as suddenly making Draco and Snape nice to him for no reason other than the whim of the author. If you want one character to relate to another in a way considerably different from usual, it's important to offer rationale for his change of heart, whether it's for purely political reasons or that he's been exposed to the other character in a new light that helps assuage preconceived notions. Even if you do this, it would be beneficial to gradually instill this change, rather than making it so abrupt in a way that puts off your audience and makes them run away screaming "OOC!" The most important thing to remember with this is that you need to convince your audience, and that simple assertions do not make something acceptable as truth. If there is an instance of revelation, your characters will each respond differently, but most (if not all) will have an emotional reaction to whatever it is that they learn, regardless of whether or not they outwardly show this reaction. For example, having Harry mention that the Sorting Hat intended for him to be a Slytherin should not make him immediately accepted by that House's members; rather, it should offer them a new perspective, and opportunities to come to understand him better.
7. Meandering Plots
If you don't know where you are going with your plot, that's one thing. But if your audience can tell that you have no idea what you're doing, then you've got a problem. It's helpful to at least have some sort of outline, even if it's rudimentary. As long as you have a vague notion of where you are going and how you are getting there, you can thread your plot. However, some stories can be entirely character-driven, and that works well for some authors. But if you aren't sure if that method of writing works for you, it's safer to stick with an outline, even if that outline changes a million times as you're writing.
8. Verb Tenses
Many authors have trouble paying attention to verb tenses and making sure they don't suddenly switch in the middle of their writing. For verb tense issues alone I would suggest that an author get herself a beta. If your audience is following along a past tense narrative only to be brought to present tense in one sudden, jarring moment, you know they are going to be disoriented. In some situations this can be acceptable, such as when a character is reminiscing about the past when something in the present demands his attention, but even then authors need to be very careful about how they handle this.
9. Anachronisms
Harry was born in 1980. iPods were not invented until 2001. So having him carry one around the halls of Hogwarts is not only impossible due to magic/technology interference, but also because they didn't even exist while he was in school. And then there are those fanfics that mention him listening to certain bands that he wouldn't have heard of in his time period. While some anachronisms can be overlooked, they make it seem like the author isn't really putting that much effort into the story, and that can turn an audience off.
10. Songfics
Burn with fire. Seriously, there is almost never an excuse for songfics. If a song has inspired the story, then that's great and you can mention it in your author notes, or include a line or two at either the end or the beginning. Or if you're going to have a character reference a song in passing, don't write out the entire set of lyrics; instead, a line or two can suffice to get your point across for why it is being referenced. But generally speaking, randomly inserted song lyrics into the body of a story are utterly distracting and don't offer much to the story itself.