1. Repeating themselves.
In high school (and sometime beyond) there are unhelpful rules from teachers relating to number of paragraphs, minimum lines per paragraph, and number of quotes per paragraph. Page length, word count, and more fit under this heading as well. Too many times I've seen students try to say the same thing in a different way in order to puff up their writing to hit a word count. It's easier to just think some more about the subject matter!
2. Trying to sound academic (or something).
Many a time I'll talk to a student and ask their opinion about some topic or relevant subject. They'll explain themselves clearly and concisely, and sometimes even with some with and humor. Then, when it's time to write, they start saying things like: "This subject is truly fascinating, as I believe that it is truly relevant for children in our society to become educated about many of these diverse and sundry topics"...BLA BLA BLA you're not saying anything!
3. Leaping without looking.
By this I mean: too many young people start writing without doing any thinking first. Grab a sheet of scratch paper and make an outline. Or better yet, before that, just start jotting down whatever thoughts pop into your head about the subject or prompt at hand. No opinion or fact is too silly for this. Then you can begin that essay proper.
4. Not reading enough.
Students: start reading for pleasure, now. If you don't read for pleasure, you are not only missing out on one of the few comforts of a dark and lonely world--you're also shooting yourself in the foot when it comes to the Reading and Writing sections of the SATs, ACTs, and relevant AP tests. By reading books on topics you care about, you will absorb by osmosis what others have to memorize with flash cards.
5. Skimping on grammar.
There are a few grammar rules that you need to know. Need. Unfortunately, most people don't know how to teach grammar in a way that doesn't make you want to undergo defenestration. Try listening to the Grammar Girl podcast, or buying a copy of Strunk and White and reading a section once a week. Or, at the very least, remember the me/I debate, the "its" vs "it's", and the other basics. If you don't take the half-hour necessary to hammer these rules into yourself, they will haunt you in workplace memos and metropolitan cocktail parties the rest of your life.