Whole books have been written about style, grammar, writing clearly, and the process of editing, so it is extremely difficult to summarize the key points. Many of these points (and more besides) will be covered in the section on print resources in our companion guide How to... prepare papers if English is not your first language, where there is also a useful section on online resources.
At proofreading stage you should be concerned not just with eliminating error, but with clarity. Much of this is already covered in How to... write more simply. Here are basic tips and things to watch out for:
Sentences which are too long and which have a sprawling construction, for example one with too many equally weighted clauses. In such cases, see whether it is possible to have two sentences instead of one, splitting the sentence at a conjunction (and, or, but).
Parallel construction of sentences: this should be both from sentence to sentence (see the section Using parallel sentence construction) and within sentences. For example, "In 1945 the Labour Government's key objectives were to create a new national health service, to nationalize key industries, and to introduce welfare benefits for all".
Avoid repeating words or phrases, as in: "If your first language is not English, you may wish to get a native speaker to help you edit as editing is much harder work if your first language is not English".
Avoid split infinitives, e.g. "To boldly go" (should be "Boldly to go").
Avoid 'sentence fragments', for example sentences without verbs, which may be all right in colloquial language but not the formal language of a research paper. Each sentence should be grammatically complete.
Some words are easily confused, for example affect and effect, lead and led. If in doubt, check in a dictionary!
Avoid dangling modifiers, for example in the sentence "The Athenians acknowledged that there were other gods worshipped by other peoples whom they did not know about". It is not clear here whether this refers to the gods or the peoples. Another common example is this sort of sentence: "Lying dead in the gutter, I saw a cat driving along". This could be rephrased: "Driving along, I saw a cat lying dead the the gutter". Always make sure that your subject and verb match.
Look out for incorrect prepositions, words such as at, with, etc. which indicate position and which also come with verbs, as in the following example: "Here we are concerned not just with eliminating error, but at clarity", which should be "... but with clarity".
Make sure that you use the right tense, and that you use it consistently, for example when describing other people's ideas, or your research methodology. Also make sure that the verb number agrees with the subject, and that you don't have a singular subject and plural verb.
Make sure that your referents are clear – for example, is it clear to what you are referring when you say "This theory"?
Avoid sexist language, such as the indiscriminate use of "he", "man", etc. to represent humankind.