What version of Quark are you using? How much of a move are you seeing?
Without more info my guess is that it's related to transparency flattening. The drop shadows are introducing transparency effects and the Quark transparency flattener doesn't do a great job. You're probably seeing stitching, where the resolution of the top item is different than the resolution of the shadow which causes just enough of a misalignment to be visible.
In versions 8.0 and earlier you could try to adjust the flattener settings to see if going to a higher resolution helps. You could also apply a transparent box with a 1% black (or less) fill over your entire page. This will force all artwork to get flattened with the same settings which might help. This can make your text look chunky and make your final file pretty complex, so if possible, it helps to move other items beside the image and drop shadow to the top of the transparent element so they don't get afffected. You might need to experiment a little.
Better yet, in Quark 8.1 or later you could try exporting the transparency live. We keep the transparency live into our RIP, but if your workflow requires flattened transparency then you can use the transparency tools in Acrobat to flatten, which will do a much better job.
You'll need to use the export to PDF feature, with the prefs set to make a postscript file instead of printing postscript to disk.
See this thread for a few more details
http://printplanet.com/forums/quark/20355-quark-8-1-native-transparency-pdf-export
Shawn