Continuity mistake: When Christopher Walken gives his wife a tape of his best memories, many of the shots are 3rd-person, of the two of them, and not 1st-person, from his perspective, like everyone else's recordings.
Plot hole: The demonstration to the Board of the system's potential is ported through acoustic modems. Even in those days (early 1980s), anyone would have realized that the bandwidth simply wasn't possible at 300 bps.
Continuity mistake: As Alex is congratulating Mike and Lillian and saying the department heads need to be told, Lillian lights a cigarette. The camera switches to Alex, who says one sentence, then back to Lillian and the cigarette is almost gone.