Adding a background map
Adding a background map could be done straight in the Data Inspector main UI. Now it's a bit tedious to go to Tools > FME Options and set the background map there.
Multiple background maps
At the moment, you can have only 1 background map at a time in Data Inspector. There should be a possibility to add several background maps to the same view.
Background map opacity
Now background maps are lacking opacity control.
Save background map for later use
When you change your background map settings, the previous background map is gone. It should be possible to save the settings in the same way you can do for Database Connections.
These problems occurred, when I was setting a WMS background map. I changed it later to a different background map, but wanted to go back to the WMS background map. I had to set all the WMS parameters again.