How can I effectively use my time when re-reading my answers?

When proofreading answers it's important to use this time effectively, if you simply skim-read your answer you will miss important changes you can make. There are obvious mistakes you can look out for carefully make sure that you haven't made any simple spelling or grammar mistakes, but in order to really improve your answer you want to proofread your work with a particular angle. A good way to look at your work is ensuring you have precisely answered the question. If you are pushed for time, focus on the last few sentences of each paragraph rather than closely reading everything.
For example if your question asked you to explore justice in Shakespeare's 'A Merchant of Venice' you may be tempted to discuss cruelty, either Shylock's cruelty to Antonio when demanding his pound of flesh or the cruel treatment of Shylock at the end of the play. You can use your time when re-reading to explain why your discussion of cruelty is relevant to the subject of justice (e.g in the ways that justice can be cruel, or whether the justice system should try not to be cruel) thus tying your answer more firmly to the question.