Most probably, one of the crucial things is attention to detail. Thoroughness and scrupulousness determine a successful editor. Be incredulous. Be passionate for accuracy.
Do not take the facts you encounter on trust. You need to be willing to double-check everything and triple-check oneself. Thus, be a fact-checker. Ask yourself: “Am I sure about it?”, “Does it fit in here?”, “Do I like how it reads?” etc.
Try to embrace and unite the text itself, the reader’s understanding and the writer’s vision. If the text is alive – make it look perfect.
You may consider reading aloud the text to be a useful tip. Repeat it several times till you are sure everything goes smoothly, the passages are connected to each other and it is easy to follow the main idea. The absolute coherency is what you should try to achieve.