There are basically five punctuation errors that every writer must avoid. These are:
1. The Comma Splice – Two sentences joined only with a comma.
Example: He fell into the pool of water, his clothes soaked up the cold wetness. This should be two sentences.
2. The Run-On Sentence or Fused Sentence – A sentence containing two complete thoughts jammed together unnaturally.
Example: Edward’s skin lit up like a nuclear bomb his face shining gloriously as if to blind the world.This should be two sentences or should be revised to incorporate both thoughts.
3. The Sentence Fragment – A sentence that does not contain a complete thought.
Example: I can find the horcrux. If I wanted to. Either combine the sentences or finish the thought of the second phrase.
4. Dialogue Rules – All dialogue should be surrounded by quotation marks (“”) and each time a new person speaks, there should be a new paragraph… unless you are James Joyce.
5. Apostrophes –
Apostrophes indicating possession:
- This is the girl’s doll. One girl owns this doll.
- This is the girls’ doll. More than one girl owns this doll.
- These are the girls’ dolls. More than one girl owns more than one doll.
Apostrophes indicating letters missing from words:
- I can’t find my hat.
- I’ll get right on that.
- It’s not okay to write about sparkling vampires.
Writing Is Hard Work 
I got the BIGGEST grin when I read “It’s not ok to write about sparkly vampires.”
Yeah. Vampires burst into flame in sunlight ala “Angel” or “Lost Boys”. They. Don’t. Sparkle.
“…unless you are James Joyce.” HAHAHA!
So glad you got that joke. Winning!
I’m with you except on the fragment. Sometimes stylistically, only a fragment will do. It’s more about cadence and rhythm at that point than about what’s ‘correct’.
That does depend on the style of the piece. However, fragments sometimes creep into writing where they are not desired by the author.