One quick tip I give to my students while editing their writing is to read their paper backwards. Usually when I say that, I receive puzzled looks, but I promise it works. When I say read your paper backwards, I mean start with the last sentence of your paper, read it by itself, and then move to the second to last sentence. Ideally, read each sentence out loud to catch any minor errors with verb tense or typos.
The idea behind reading your paper backward, sentence by sentence is to break the "flow" of your paper. As you read it normally, you start to get into the flow of your ideas and sometimes what you think you're reading in your head isn't exactly what's on the paper. If you break the flow, spotting little errors becomes much easier because you're focusing on sentence-level issues. This should be a final step in the editing process; it won't necessarily help with larger organization issues.
So remember--before you finally hit "print" or "submit," make sure to read your paper backwards!