Several basic suggestions.

First, put your manuscript into a drawer, and forget about it for a couple of months. You will discover a whole lot of exciting new things when you take it off from the drawer and re-read anew.

Second, I found that 80% of all mistakes are conveniently marked by the authors with the words like 'evidently", "clearly", and phrases "it is easy to see" etc. Double-check all occurrences of these words/phrases in your manuscript.

The final suggestion: make your manuscript public. Post it to the arXiv, mail it to a colleague, submit it to a journal. You are guaranteed to find a bunch of mistakes in the following ten minutes.