Symptoms

When adding the K2 SmartForms Web Part on a SharePoint 2013 site collection, it doesn't show any worklist items.
 

Diagnoses

This was a bit of a difficult issue to diagnose due to some language barriers and a lack of understanding how the product works, but eventually we got to the same conclusion.

We first tried to analyse why no worklist items showed in the K2 Worklist Web Part. We ran a Fiddler trace and looked at the K2 logs, but no apparent reasons jumped out.
 

Resolution

We finally came to the conclusion that the way K2 displays forms in a web part has changed from SharePoint 2010 to 2013. What I mean by that is, in SharePoint 2010 you would view the web part's properties and specify the K2 URL to use there.

However now with SharePoint 2013 the method has changed, where now you just add the K2 Forms Web Part to a site collection, save and publish the site, then the newly created K2 Forms web part would just display a toolbar at the top akin to "Quick Search", it looks suspiciously a lot like the old K2 Worklist web part for SP2010.

In this case however, you would then have to use the Quick Search to search for your Form name and finally select it. When that is done, K2 would then display the previously selected SmartForm permanently, without the user having to edit the Properties or Advanced Settings of the web part.

I have linked this ticket to a documentation feature request to improve the wording on the K2 Forms Web Part for SP2013 to clearly indicate the next steps on how to view a Form. This is especially true for non-english speaking customers or where there is lack of training.