Symptoms
Certain users cannot access Worklist web part. Access Denied
Diagnoses
The issue here is the user needs read right to the App catalog.
http://help.k2.com/onlinehelp/K2Appit/UserGuide/current/default.htm#About_K2_for_SharePoint/CompatSecPermConsid/K2_Application_Permissions_in_SharePoint.htm
Resolution
Granted Read rights to the App Catalog.