What can break quickedit, and how do I fix it? We hired someone else to make our theme, and they gave us something with the quickedit not working.  What can cause this to break, and how do I fix it?

Here's what my contextual-links ul looks like right now:

&lt;ul class="contextual-links" hidden=""&gt;&lt;li class="quickedit"&gt;&lt;a href="" role="button" aria-pressed="false"&gt;Quick edit&lt;/a&gt;&lt;/li&gt;&lt;li class="entitynodeedit-form"&gt;&lt;/li&gt;&lt;li class="entitynodedelete-form"&gt;&lt;/li&gt;&lt;/ul&gt;

The entitynodeedit-form li is empty, as well as the delete li.  What is supposed to fill them in, and how do I fix it?
If there is not an obvious error in php or javascript, see the comment from @mradcliffe, then there are probably some attributes missing, because they were removed in twig templates.

The quickedit links are not delivered in html, they are build in javascript. For this the attributes to identify the involved entities and fields need to be present.

Look especially for the attributes data-quickedit-entity-id in node templates and data-quickedit-field-id in field templates. 

This is the correct way to add attributes in twig:

{%
  set classes = [
    'red',
    'green',
  ]
%}
&lt;div{{ attributes.addClass(classes) }}&gt;&lt;/div&gt;


Source: https://www.drupal.org/docs/8/theming-drupal-8/using-attributes-in-templates