I find it efficient to make several passes through the all papers. Although it would involve reading each paper more than once, I find I am able to give them better focus and achieve better results, which I will explain.
In the first pass I check for very basic things, such a rubric, have they been labelled correctly in the correct basic format; I check for typos, spelling, citations, bibliography and note anything messy and distracting. Having got those out of the way I find I can now focus on content without being constantly distracted by flagging the visual aspects. I read (scan) through all the papers only handling the trivial aspects. Once done I start again on the next pass.
In the next pass I focus on the reading and ensure the sentences and paragraphs make sense. I can pick up missed words, malapropisms, homophones, punctuation and such like this way. Once I am happy that the words make sense on a micro scale (in all the papers), I can start to look at the bigger picture.
On the third pass I can look at overall structure; is the material introduced in a sensible order, is the focus on the right area and finally did I enjoy reading it and did overall make sense.
It might seem long winded, but I find that my performance (scripts per hour) can be faster and more detailed than myself or compared to colleagues that note everything in one script before moving to another.
This may not work for others, but I offer it as an example methodology.