Symptoms

Customer is using the K2 Worklist Web Part in SharePoint 2010.
A client event is configured with the Destination Rule > Plan per Destination "All at once", and Destination Rule Options "Create a slot for each destination" and "Resolve all roles and groups to users".
If one user opens the event, but doesn't action it, all the other users in the group get an additional line item in the K2 Worklist in SharePoint. It is the same information, but the check box is greyed out and the status is allocated. When I try to open the task, it says I do not have permission.
 

Diagnoses

What you are seeing is expected behavior, based on filters.
When you have all at once, and multiple slots, a worklist item exists for each destination user. When one user opens their worklist item, their copy is changed to "Open" status, and everyone else's becomes "Allocated".
You should be able to define a filter that will hide Allocated items.
 

Resolution

Here is the documentation on using filters in the K2 Worklist for SharePoint:
http://help.k2.com/onlinehelp/k2blackpearl/UserGuide/4.6.9/webframe.html_K2_Worklist_in_SharePoint.html
http://help.k2.com/onlinehelp/k2blackpearl/UserGuide/4.6.9/webframe.html_K2_Worklist_Configuration_-_Filters.html