Hi!

To see what I meant, create a new buffer with "C-x b", then paste the
same text there, after setting the left fringe width to zero.

Yes, now I see it. (However, the continuation characters disappeared when L2R text was entered on the line before the R2L text.)
 

> Also, I noticed that `window-max-chars-per-line' does not take into account the variable `left-frame-width' (and
> presumably `right-frame-width').

You mean left-fringe-width, I presume?  Yes, that's probably a bug.

Yes, I mean `left-fringe-width'.

 
Why is this useful, when we already have window-max-chars-per-line?
IOW, when would you like to know about the continuation glyph, and not
about how many characters can be displayed on a line?

I intended it as a way to implement `window-max-chars-per-line' in a more robust way than today.

In addition, I can think of a use case. If you want to create a window of a specific width, excluding the continuation glyph, this can be used:
   
   (split-window-right (if (continuation-glyph-visible-p (selected-window))
                                  (+ width 1)
                                width))

    -- Anders