I haven't written in many years; but back when I did I used to think sort of like you did. Then in a creative writing course, I was directed to Stephen King's "On Writing" as a source of potential advice. While most of the book is a quasi-autobiography explaining how he got into writing, it does detail quite a bit of his writing process.
Simply stated, he'll sit down and write, write, write until he's got nothing left. Grammar, spelling, plot holes, etc are completely ignored. Once it's all down on paper, he'll give it a cursory spell check, and then throw it in a drawer (he writes on paper a lot). Once it's in the drawer, he doesn't look at it for a full month or more. Basically, he waits until he's actually forgotten a lot of what he's written. At that point, he'll take it out and read it. After reading it is when he starts making the decisions on what to change; even entirely scrapping stories that just don't work for him.
I started doing this process as well, and I found it was extremely helpful. Seeing the story quite awhile after writing it not only helps tremendously with finding the small problems (like grammar), it also helps with the larger story as a whole. Does it make sense? Are there glaring plot holes? Did you enjoy reading it? It can give you an entirely new perspective on the piece.