Try the Press pdf export preset and click on the Advanced section. Transparency flattener should show High. See if that helps the banding (targets) of the thing.
The white lines are a mystery. I would make sure I didn't accidentally have something in there - like a white line or something. Try Select All in ID and see if anything shows up. Also, what does the curved object consist of? That could be important - lile combined paths etc.
To test, make a new ID doc, type some text and then draw a rectangle or elipse somwhere else on the page. Apply the drop shadow to the text box and the shape. Export the pdf at Press - making sure that it shows High in transparency flattener - and see what it looks like. If the whaite lines are still there, you have some sort of other problem. If they're gone, you have a problem with the shape you originally used.
Using OSX 10.3.9 on a G4