Result: There's one single entry: debug.showErrorsInStatusBar: false

I don't understand why you think this is a problem. By not writing it to the prefs file, then you have to set it every time you open Brackets, right? I think that's worse because it requires me remember to do more work (and then actually do it).

I, personally, would prefer that the default for this feature to be on, but the team was concerned that this would unnecessarily alarm non-coders, so the default is off.

You misunderstood the problem :)
In a fresh Brackets installation, there are no prefs set (the brackets.json is empty), except debug.showErrorsInStatusBar.

If the menu entry changes, the pref is still saved.

Oh, I see. I don't think a new parameter is needed for that. What if the code only writes a new pref if it's different from old pref?

I've taken that approach from the QuickView code.
The problem with only setting the pref when it's different is that you can't set it to "explicitly false".

By "different", I meant the pref values converted to boolean, not the strict value.

Done.

Looks good. Merging.