How do I spot and fix continuity errors in my story?

I just finished a very rough first draft for a story I am writing. The draft has around 80 typed pages or so and has 6 chapters.

What I want to do now is to go back and look for continuity errors. By continuity errors, I mean:

(1) Discrepancies regarding the same person/place/thing (e.g. calling a character Bob in one chapter and the same character Bill in a later chapter without any accompanying plot twists)

(2) Timeline impossibilities/improbabilities. (e.g. A person having two birthdays)

Any tools/techniques/approaches you use as a writer to spot and fix such mistakes?