peer review - How can I Get a Job Reviewing Math or Comp Sci Articles and Books in Advance of Publication?

I spend a great deal more time than other graduate school students identifying and figuring out how to fix mistakes in published papers and specialized books. Time and time again an author's careless error has sent me down a rabbit hole. In fact, finding the mistake and fixing it is often more interesting to me than the research itself. It dawned on me that I might be able to make a career out of editing working papers and books in advance of publication. However, I am not quite sure how to find such a job.

I am not seeking to publish my own research; I prefer revise and improve others' work. It seems like a useful thing to do: Author's mistakes becomes my personal headache, so that a dozen or more readers down the line do not have to independently run into the same issues (after publication). It is better to fix this sort of problem at compile time rather than run-time.

However, Most peer-reviews are unpaid and done by collegiate professors. I am not seeking a professorship; I don't even have a Ph.D. The highest degree under my belt is a baccalaureate (It is in mathematics at the very least).

When I took the GRE, I was in the 98th percentile for verbal reasoning. This and other indicators seem to show that I might be a good copy editor. However, I really would like to review papers in mathematics and/or computer science. Although editing at The New York Times, or at Tor Books™ might be someone else's dream job, I very much love math. I would like to focus at least as much time on the rigor and correctness of the mathematics done, as time spent on English grammar.

I am very good with logic (the formal kind), comfortable writing proofs, and unperturbed by mathematical symbols equations which make the general populace groan. I am better with graph theory and theory of computation than writing code; my math skills are strong. I have no previous job experience as an editor (other than a pitiful stint at my high school newspaper) and I am not sure where to start looking. I spend a great deal more time than my peers (in graduate school) identifying and figuring out how to fix mistakes in published papers and specialized books. Time and time again an author's careless error has sent me down a rabbit hole. In fact, finding the mistake and fixing it is often more interesting to me, than the research itself. It dawned on me that I might be able to make a career out of editing working papers and books in advance of publication. However, I am not quite sure how to find such a job. A penny for your thoughts?