Robert Scheitlin provided an answer over on the ArcGIS Viewer for Flex forum. Link:
http://forums.arcgis.com/threads/36322-FlexViewer-2.1-Add-scroll-for-widgetgroup
His answer:
"Sure just find this block of code and make the changes indicated in red in the HeaderControllerWidget.mxml:"
<s:BorderContainer id="widgetList"
x="{xOver + 4 - widgetListDG.width/2}" y="{headerContent.height}" width="{widgetListDG.width + 29}" height="300"
backgroundColor="{getStyle('contentBackgroundColor')}"
borderColor="{getStyle('color')}"
borderVisible="true"
cornerRadius="3"
rollOut="widgetList_rollOutHandler(event)"
visible="false">
<s:Scroller width="100%" height="100%">
<HeaderController:WidgetListDataGroup id="widgetListDG"
width="150"
dataProvider="{groupWidgetAC}"
visible="{widgetList.visible}"
widgetListItemClick="widgetList_widgetItemClickHandler(event)">
<HeaderController:layout>
<s:VerticalLayout paddingTop="6"
useVirtualLayout="true"
verticalAlign="middle"/>
</HeaderController:layout>
</HeaderController:WidgetListDataGroup>
</s:Scroller>
</s:BorderContainer>
Since the red doesn't appear here, I needed to add the <s:Scroller>
parts, and modify the widgetList properties to width="{widgetListDG.width + 29}" height="300"
.