When ArcGIS.com Web maps are opened in ArcGIS Desktop 10, two layers called ‘Base Layer’ may be listed. One of the layers is a reference overlay that should be drawn on top of the other base layer in the map. In some cases, the two base layers may draw in the incorrect order.
Some basemap layers available through ArcGIS.com include a reference overlay. One example of such a basemap is ‘Imagery with Labels’, in which case the labels are a reference overlay on the imagery service.
In some cases, the imagery layer may be drawn over the labels reference overlay when this basemap is consumed in ArcGIS Desktop. This is a known issue with ArcGIS Desktop 10.