This is really strange. I'm using a private browsing session to rule out browser cache. I have observed this on multiple computers.
In one particular sub menu where I created new links, then edited them, whenever I refresh the page I get one set of links and when I refresh a second time I get another set of links. So it's the original links I created then the links I edited that alternate.
I don't have side navigation menus so I couldn't say if it's happening to them too.
In the site nav settings I have this option selected for global navigation, Managed Navigation: The navigation items will be represented using a Managed Metadata term set.
Not sure why this is happening.
Thanks,
John