Self-editing is a must for all writers. After finishing my first draft and even while writing my draft, I run through many revisions. A great book for self-editing is Self-Editing for Fiction Writers. This book and other resources will give you plenty of pointers on what to look for while revising your manuscript.
I also believe that each author has her own quirks while writing first draft and things that she may forget to take care of. These quirks will not be spelled out in any book. These are things for us to remember for ourselves. What I really find useful is keeping a revision checklist that I keep updating as and when I come across any quirk of mine. This running checklist is a great resource for me to feel confident that I have taken care of things.