For both puzzles, I considered the alternatives, and thought: well, if the text itself doesn't disambiguate the solutions, what would be the most reasonable assumption I can make to arrive at a single possible solution? For the watchmen that's assuming that Bernie's talking about his own shift; otherwise, why would he even be at the factory to hear the explosion? For the arm wrestling competition, it's assuming that it's a knock-out tournament.
But I do agree with asfm that this takes it outside the purely logical realm, which also makes it hard to reason about the problem rationally. It would probably have been better to avoid these ambiguities. But I don't think either puzzle is completely "broken".