What is (arguably) the single most important thing to know about proofreading?

Answer 1

Rather than one most important thing, I would say there are two equally important things:

1. I agree with the previous answer: long essays, papers or documents need to be done over multiple sessions for the highest accuracy rate.
2. The proofreader must go slowly and carefully, reading every word, looking not only for grammatical, spelling and punctuation errors, but also for words which are written twice, e.g. "I gave the the milk to my friend to help him out" where the word 'the' is written twice.

Answer 2

It can't be done completely, by one person, in a single pass or session. For a document with any more than a few words, multiple passes and multiple sessions are needed in order to do the job conscientiously, catching at least close to all errors.