I’ve noticed that when I’m in my office going through a piece of work with a student, as they are sitting there with me they often find lots of mistakes themselves. Even though they wrote the essay, now they are seeing it again more objectively, as if for the first time, and they find the mistakes they didn’t see before. If you can try to see your work objectively like this, you will find errors which you missed when you wrote it. I’ve got two suggestions for helping you check your work to find mistakes.
The first method is to read your piece of work checking only for ONE particular type of mistake each time. You should know what type of mistakes that you most commonly make - for example subject-verb agreement mistakes, mistakes with articles,singular/plural mistakes, mistakes with tenses. Decide which type of mistake to check for first (eg subject-verb agreement) and then read through the essay checking for ONLY this type of mistake. If you are doing subject-verb agreement start with the first sentence and find the subject. Is it singular or plural? Countable or uncountable? Now find the verb that goes with this subject - is it in the right form to go with the subject? (For more on subject-verb agreeement and a nice exercise on this see my post Subject and verb agreement archived on the right-hand side of the page.) Go on to the next sentence and do the same, and so on through the piece of work. When you have done that you choose the next type of mistake, maybe articles, and you go through the piece of work checking just for article mistakes. Then you do it again with the next type of mistake and so on.
Phew. That may take some time but your work will benefit from it. What you are trying to achieve is objectivity when you look at your work. The problem is that you have been so involved in it that you cannot see it with new eyes. So my second method is to suggestion is that you check your work by reading it backwards. Sounds rather odd! What I mean is that you look at the final sentence first. You begin at the start of the final sentence and read it checking for mistakes. Then you move back to the next sentence and check that one, and then the one before that. The reason for doing this is that when you do this you take the meaning out of the sentence and you check it just for its grammatical form. When you read from start to finish you are focused on meaning, and it is really difficult to try and ignore the meaning and focus just on the grammar.
Try putting these two suggestions together!