I have an issue with the not being able to edit the QuickLaunch navigation which only occurs on publishing pages (pages created based on page layouts) not system pages.
The issue is that when I am on a page created based on a page layout(publishing page) and I click on the 'Edit Links' at the bottom of the QuickLaunch section I am not able edit the links on the QuickLaunch menu. (the page layout was created with SharePoint Design Manager)
Usually when you click on a link in the QuickLaunch menu while it is in edit mode a text box is shown and you can edit the link (see second image below), but in my case this is not happening for publishing pages, hence you are not able to edit the links via the QuickLaunch menu. (see image below)
The image below is an example of 'edit links' NOT working on a publishing page:
The image below is an example of 'edit links' working on a system page:
NOTE: Both images above are from pages using the same master page (Seattle Master page, SharePoint 2013, Site Collection Publishing Features Enabled)
I have been able to reproduce the issue with multiple publishing pages based on different page layouts.
Update: This issue occurs on all browsers (IE, Chrome, FF, Safari)