The fact that they were created in 2003 might have bearing here.
You might try reapplying the slide layout to the affected slides. Also head
to master view and make sure the shadow is added to the placeholders on the
slide master (the big one at the top) and that the placeholders on the
individual slide layouts beneath the master inherited that shadow properly.
If you end up with empty placeholders (click to add) after reapplying the
slide layout, then the textboxes were created manually, and that would
explain why the shadow doesn't apply properly.
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