I think it depends just how many errors you are making and how trivial/non-trivial they are. I agree with the poster below, saying that checking and double-checking is one good way of tracing errors before anyone else does. However, I believe, that we are all making errors, and not all are found, even by supervisors/reviewers etc. As a suggestion - aim to be focussed at all times when you do important work, and when that is not possible, choose to do tasks that require less focus and attention, or break up the work in smaller sections and take regular breaks to stay sharp.
Hope that helps... all the best.