The left nav menu on a 2013 site has begun misbehaving. A week ago it worked perfectly, but now whenever I use the "Edit Links" button, several symptoms appear:
1) All links appear with an "x" next to them instead of some having the "show/hide" icon.
2) The "x" does nothing when clicked (can't delete links).
3) Links cannot be re-arranged.
4) Link names cannot be edited by clicking next to their text.
Once in a while (cannot pinpoint why) when I click "Edit Links" everything works as normal. But the vast majority of the time it is afflicted with the symptoms described above. Repeatedly closing/opening the edit menu does not seem to change the results. Clearing cache and/or refreshing the page do not change results. Using different browsers does not change results (it either works on all of them at the same time, or is broken on all at the same time, so it looks to be a problem internal to the site).
I can't find any other instances of this online, though it's tough to search for considering the strange symptoms. Has anyone else ever seen this, or does anyone know where to start troubleshooting?
Edit: As requested by Magali here is a screenshot of the menu while it is misbehaving. Several of the links are supposed to have the visible/hidden icon instead of the "x" and at this point links can be dragged around but when you drop them they just go back to their original position. The "x" is non-functional (cannot delete a link) and they also cannot be modified.