How to Improve Spell Check?

What I wanted was some demonstration of a misspelling not being identified.

The settings are for you to review on your own. What you want to use is the "Show Spelling and Grammar" option. That will show what language your spelling is configured to use. If it is set to the default "Automatic by language", then it will accept any misspellings as long as they are spelled properly in some other language.

All of this depends on your regional settings and what you are typing. There are some heuristics. Here is a simple example showing one misspelled word in English and a correctly spelled phrase in French:

Here in Canada, enrolment only has a single "l".

From your Edit menu in the application, select Spelling and Grammar > Show Spelling and Grammar. Change the selector that by default says Automatic by Language to your explicit language (e.g. U.S. English, Canadian English, etc.). You may want to also change this in System Preferences > Keyboard > Text panel too. This has been known to provide more accuracy with spell check.

Another alternative is to install the free Grammarly application for macOS. It works on Monterey and Ventura just fine. I have done this without creating a Grammarly online account and it will watch my text input for spelling errors, or if it is wrong, allows me to dismiss that check.

In my experience the only thing you can do to improve the spell checking (aside from installing a third party version) is to use the "Learn/Unlearn" spelling options. See Check spelling and grammar on Mac for details.

I can't remember it missing any obvious errors, but it doesn't try to interpret what you mean with spelling. It seems to just have a limited matching dictionary with no (or maybe limited) ability to guess based on the spelling used.

If you can provide some examples, I'll check to see what I get.

Can you provide an example? And review your spell check settings to make sure they are correct?