What's one of the easiest edits a writer can make to his or
her work to improve his or her chances of getting published?
Changing most of your passive voice sentences to active voice will strengthen your writing immeasurably. What do I mean by that? The screen-cap below sums it up better than any grammar book ever.
The dog was groomed (by Zombies) yesterday. -- insertion works, therefore passive
Zombies groomed (by Zombies) the dog yesterday. -- active, there insertion doesn't work