As you've noticed, if you change a page's Menu Title then Save and Publish, the URL stays the same. This is intentional so that URLs don't change willy nilly and you end up with a website with lots of links to pages that don't exist any more!

However, if you first unpublish the page (from the Publishing tab), and then Save and Publish it, then it'll be given a new URL from the Menu Title, which can have the correct spelling in it.

Thanks

Joe