Sandra,
The group task thing troubled me a lot too.
I dont know whats wrong with your impl but this is what I do :
//Connect the task handler
BlockingTaskSummaryResponseHandler summaryHandler = new BlockingTaskSummaryResponseHandler();
ArrayList<Object> groupTaskDetail = new ArrayList<Object>();
List<TaskSummary> tasks = null;
List<String> groups = getGroupsForUser(userId); // Get the group IDs for the target user..
client.getTasksAssignedAsPotentialOwner(userId, groups, "en-UK", summaryHandler);
tasks = summaryHandler.getResults();
Regards.