I often do editing work. These thoughts evolved out of some recent commissions. Note that with anything artistic, there are going to be cases where the rule should be broken, but it should always be intentional and for a reason, not just because of bad habits.
  • Openings checklist. Does it establish the scene and the characters? Does it set up some mystery and potential for the future?
  • Don't use unnecessary words. Writers don't need to cover every transition, to telegraph every action. Let the reader do some work. Remember this if you have a habit of describing every time a character walks across the room, or that they "went down the stairs and left the building": that's often unnecessary stage direction. The change of scene to an outside one often makes it inherently clear that the character went outside.
  • Never miss chances to show rather than tell. "She walked quite fast." Avoid "quite" and weak adjectives in general. They add nothing. Even better, tell us how someone walks by showing us, rather than telling us. Did her arms swing like she was marching? Did she look down as she barged past people? Did the other pedestrians blur by because of the pace she set? Another example: "A pretty woman walked in." Bear in mind that "pretty" can be a weak word. In what way is she pretty? What was so attractive about her in the character's eyes? Show us, don't tell us; then we'll feel it ourselves.
  • Don't use unnecessary words. Again. Don't say something then have another sentence where you rephrase it. Nine out of ten times it isn't something worth that level of repetition. Every unnecessary word added just waters a story down.
  • Avoid infodumps. Especially near the start. There's always a better way.
  • Make settings live. Give readers non-cliched details of the places where scenes are set, so that they stand out from each other and come alive. If the story is set in Paris then make us feel like we are in Paris.
  • Unintentional comedy. "The dark chocolates were so rich they made my spine quiver." Did they really? I like chocolate, but haven't experienced that. Beware of unintentional hyperbole that might lead to bathos. No problem if it is a comedy piece, but not if it is meant to be serious. Remember the tone.
  • Real voices. When you're creating a character's voice, or viewing from their perspective, give it some life! Combine action and sentiment with punchy, living rhythm. It's okay for a character to talk and think as people actually speak. Too many stories are written as if Dickens was checking over the author's shoulder.
  • Don't miss an opportunity to surprise the reader with a twist or a question or a hint of mystery. I don't mean you should add them for no reason, but sometimes a beginning writer includes an element that makes the reader prick up their ears - then does nothing with it.
  • Make words work. Short fiction makes every word and image important, so if either of them can do double duty, and work harder, it helps make the whole stronger and more unified. Think about your imagery and the relationships between words.
  • Don't use unnecessary words. Yet again. "He laughed out loud." You don't need "out loud": unless otherwise stated, the reader will assume it was out loud. Only add stage direction when it goes against expectation. Likewise "She tilted her head a bit" - do we need "a bit"? I wouldn't assume it was a 90 degree snapping action without that. Both are examples of cutting unnecessary words. 
  • Capitalising roles. "Howdy, I'm a Bank Manager." No need to capitalise general jobs. Someone is a teacher, a chef, an accountant.
  • Endings are often the hardest parts to write, but also the best chance to one-two the reader and leave them dazed but somehow loving it.
Just in case you wonder: any quoted sentences above were just ones I made up for illustrative purposes.