I recently received an 88% on an essay in a second year social psychology course. The Prof's remarks gave the impression the organization of the essay was key.
"Good use of headings and organization of information. Your paper was very easy to follow and the perfect length!"
Often, especially in social sciences, we want to write in a poetic or otherwise "interesting" way, but concise and methodological organization will get you points with the marker.
Always aim for the maximum length or slightly less, while still being concise. Edit out everything that isn't necessary. For a 2000 word essay, I've often written 3000 only to edit out 1000 unnecessary words. Minimum length essays tend to get lower marks.
Do some relevant "above and beyond" research, rather than just assigned readings, to show you've really done your work. It can also help you to add novel points in your paper that other students won't have. Creative angles that distinguish your paper from the possibly hundreds of other essays, a mark of idiosyncrasy, will definitely help your mark. Engage deeply and critically with your sources rather than superficially touching upon a large number of sources.
And of course ... use an online grammar checker (even if they are limited). Get somebody knowledgeable to do a proof-read if possible.