Hi,
A couple of questions:
1. Does the mini print preview look ok?
2. If you click the Copy to clipboard button (Home Tab) > then paste into another application - how does that look?
If the map within ArcGIS Explorer looks fine but #2 above looks bad then I'm uncertain what to suggest because it's effectively doing a print screen operation. For any display issues however, we usually suggest updating your graphics drivers as the first thing try.
Regards
Mike