Hello Ken, I'm not sure I can help you as I'm not sure what a 'blue globe wireframe' is exactly. However, you've described it as a flattened .png.
So are you attempting to add a drop shadow to an asset .png file within your Fireworks working file?
Nb. It is unusual to flatten a .png file, because .png files are used for transparency and flattening should remove that quality. I use CS4 Fireworks and a PC, and I have attempted both a flattened .png and a normal one. These image files were imported into the document, onto a particular page and then their own layer. Additionally, I right clicked the none flattened .png and was still able to add a drop shadow.
Make sure you have done your housekeeping and know that the asset you are attempting to add a Drop Shadow to, is highlighted on the layers panel and that you are on the correct page. Also, ensure that the layout view is in Iconic Mode [top right]: which means all panels go to icon and the Properties Panel is in full view.
For PC, highlight asset, go to Properties, click the tiny arrow key next to the + sign, find filter. If this doesn't work for you. Then give more info about how you created the asset,what operating system you use and which version of Firefox. Hope this helps. Sometimes all the Adobe programmes can sort of get stuck. So just close doc and open again, and hopefully, should clear up the bugs. Best wishes