Factual error: A 250-year-old sea chest recovered from the ocean floor is opened, and all its paper items are perfectly dry: the log book can be opened and read, and the letters can easily be unrolled. Highly unlikely. The chest's wood and pitch would deteriorate (salt water is extremely corrosive), and the paper should be damp and crumbly, at the very least. Even more likely, it would have become a lump of unreadable sludge.
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Answer: Late one night, Geoffrey used a covert listening device to overhear David explaining his barricade device to Janet which is how he figured it out.
How do we know Geoffrey really did use a covert listening device? They didn't mention him using one.
There was a scene of him using it when David told Janet about his barricade.