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When I'm reading something, I immediately pick up on typos, grammatical errors, misuse of punctuation, and the like, as well as better ways to phrase things. I have no formal education in any sort of writing or English other than GE; my education is in engineering.

Is there some way to monetize...proofreading? Is what I described what an editor does?

One option that may work for you is Fiverr.com

I have not personally used it yet, but I plan to both hire audio editors from it, and also offer my own services.

There are articles about writing for it, but many of those also have tips aimed at editors, too.

I found some articles in a quick google about writing for it - I was looking for actual and recent experiences. One I found was http://www.financialfreedomnow.org/5-best-fiverr-freelance-writing-tips.html

With a name like Fiverr you may think that there is a serious limit to the amount you earn on this site, but in fact the opposite is true. Freelancers can (and often do) earn more than $5 for their writing services on this site and adding on additional services is a great way to increase your earnings while providing value to your clients. For example, if you charge $5 for editing a document, you could put up parameters such as, $5 for every 500 words, or something along those lines. This allows potential clients to easily digest your price structure (one of the best features of freelancing on fiverr.com) and it's a fair way for you to ask for more money for larger projects that will likely take more time

The only way you will earn money on Fiverr is if a client likes what you have to offer. The only way that they will like what you have to offer is if you are specific. They have a specific need and don’t want to waste time searching and talking with people who may or may not offer and fulfill the need they have. There are thousands of people offering writing and editing services on Fiverr.com so the key to separating yourself from the herd is to make your profile on Fiverr very straightforward so potential clients can hire you with confidence. Think of what questions you would have if you were hiring a writer, and then answer them in a FAQ section. The clearer you can be, the better.

This may be a great way to build up experience and reputation, and from that you can more confidently charge higher rates to individual clients with your own Editing Service.

This article explains how he uses Fiverr without underpricing himself:
https://learntogrowwealthonline.com/how-does-fiverr-work/
This article describes how someone chooses what to call a "gig" for their prices:

Truth be told, fiverr is suitable for anybody who is willing to do a small amount of work for $5.

The way I plan my gigs out is determining how much I want to earn in an hour, and then dividing that down into what I can do in 15 minutes.

I bill myself out at a minimum of $20 an hour, and can writea 500-word blog post in less than 15 minutes.

Therefore, $5 for 500 words is reasonable to me.

He also explains some of his organization techniques, because:

My repeat customers are the ones that really pay the bills, and you won’t get repeat customers without timely and quality work.

Of course, you'll need to figure out your editing speed, and what kind of editing you are best at -- technical, fiction, resumes? Proofreading, or bigger, structural issues?

I would say that you could definitely monetize your skills! At the very least, you could offer freelancing services. It might be difficult to get started at first, but once you get the first few clients, you'll be able to advertise previous work and pick up more and more people. Consider potentially offering services for free or at a lower price on a trial basis at first, and then adding/increasing prices later on.