Karel,
First, I would like to get to the bottom of the unspecified error. It sounds like the web part is causing the generic SharePoint error page to be displayed is this correct? If so, would it be possible to search your SharePoint log files for the text bWareTech.UserTasks to see if a more detailed message can be located? Generally, the SharePoint log files may be found on the physical file path C:\Program Files\Common Files\Microsoft Shared\Web Server Extensions\12\LOGS. If you can generate the web part error on a new page then you may be able to locate a detailed message in the latest log file. If you can spot the text bWareTech.UserTasks in the file and you prefer, you may send the file to Support@bWareTech.com and I will investigate. I can use this column in the display grid without issues in my development environment so this is an immediate concern. Also, are you still using your own language resource file(s)?
Now the Assigned To column, a quick search on the Internet will turn up many issues with the SharePoint SPSiteDataQuery when using this fieldref. So much so that the latest User Tasks Web Part documentation does include a warning about utilizing this field in filters and sorting under Administrator notes. If the web part retrieves Task items from Lists that have different settings for People Only or People and Groups then specifying a sort using the Assigned To column will cause some query failures regardless of whether the Assigned To column is being displayed in the view. While this is a known issue, I left the column available for use under the assumption it would be corrected in a future patch. Unfortunately, the issue is still present in the latest SharePoint 2010 version I am testing. If you are using the Assigned To column in the Sort definition, please remove it to see if the problem is resolved.
I may need some additional information on your second issue. The web part should properly retrieve a Task item if the user is included in the Assigned To field and the web part is configured to filter on Assigned To the User Above regardless of whether multiple user accounts and groups have been assigned to the task item. I can confirm this to be working in our test environment. However, please note that if the current user is part of a group that is the Assigned To for a task item that task item will not be returned in the results. This behavior is identical to the OOTB User Tasks Web Part.