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These are just off the top of my head:
"The Conversation" (Francis Ford Coppola).  The entire plot revolves
around the protagonist's interpretation (or MIS-intepretation) of a
recorded conversation.
"Blow Out" (Brian DePalma).  The plot centers on a recorded SOUND (not
a person's voice, but maybe that's an idea).
Some of the information about Colonel Kurtz in "Apololypse Now" comes from
a tape of his radio broadcasts.
That's all I can think of right now.
-- Kirk