I critique stories for my homeschool groups writing club, and other stories, and this is what I'm seeing a lot of:
Starting out with TRUCKLOADS of angst
This is called an "Angsty Sue", and starting with 10 italicized pages of her inner torment, eating disorders, and how she wants to kill herself isn't going to make us care about her. We live in a jaded culture, and if you want to make us cry, at least tell us her name and what happened to her first! "I stared at my crystal chandelier, smartphones, and really expensive clothes, wondering where to go. Life is so unbearable, I wish I could just sink into my satin comforter and die....."
No. Please no. Most stories start out simply, quietly and nicely. (but NOT boringly.)
Including tons of description
This is mostly a girl problem. We love to add tons of description about our characters beautiful red hair, pooly-cerulean-green eyes, nose, mouth, feet, and don't get me started on her clothes! Believe it or not, no one but you really cares about what your character looks like(in normal stories.) Use concise, creative words and phrases to describe characters. What character descriptions really do best is to give you a foreshadowing description of the character(She had gray hair tied into a strict bun, and a burn scar on her cheek which only served to intensify her scowl.) What does this tell you about the character? Is she the doting, compassionate, village woman who shelters your main character from the storm and feeds her soup? She could be! Appearances serve for natch. Mostly, describing your character does not count as characterizing your character.
Not having a plot(NaNo is the exception)You'd be surprised at how many people start out without this very important thing. You need this. No one cares if you have a beautiful character with a really creative name if she does nothing. I'd think this was a given.
Not characterizing enough
What's characterizing for? To make people feel something about your character. We need to sympathize, enjoy, or respect your main character in order to care what happens to her! We know you care about your character, but you have use your story to make us care, too! It's not magically going to happen.
"Telling" too much
This is a really tough category to fix and be in. Sometimes "telling" is enough, sometimes it isn't. Many authors like to start from the "bare-bones" of the character and build layers of detail on by showing what the character does in certain situations. Phileas Fogg(from Around the World in 80 Days) is a great example. Jules Verne captures readers attention without telling much by showing Fogg's strange OCD fascination with time. Verne captures Fogg's patience and compassion when Fogg is patient with Passepartout and gives money to the poor woman.
Showing people your novel when its not finished
This isn't wrong, but if you're writing a serious novel(NOT for fun) you want to be careful. I can guarantee if you're trying to publish, the first couple pages aren't going to be in the final draft. Your first words are bumbly, clumsy, "writing stutters". You're probably going to be revising them plenty. You certainly don't want to show your writing stutters to the world(or your mom). And don't tell anyone the plot, especially if you're going to be showing them your book. You want them to be moved and touched by your book. The chances of that happening are greatly diminished once you tell them the summary.
Not making your novel unique
There are tons of books in the world. Give your readers a reason to spend their valuable time reading yours. Parodies, satires, and spin-offs are funny, if you tell them with a unique voice that sets you apart.
Word about fanfiction
It's a great way to start writing. Pre-developed characters! A great plot to start off on! You can incorporate your own characters! The thing: Unless you're on, fanfiction.net, you will not be published for this, and it's illegal for you to earn any money from it. Even if you contact the licensing company and beg them to publish it, they're not going to.
The publishing world is vast and difficult. Even the most experienced, creative writers paper their walls with rejection slips. Most writers who write for a living started out being broke, not having running water, and eating spam every night. Are you willing to do that?
You're going to get criticism, from others and myself. My favorite people to critique are those who gracefully thank me, rip apart their book, and sew it together in a fashion that amazes me.
Will I critique your writing? Sure, but you probably won't be very happy about it.