Other mistake: When the children run into Captain Sham (Count Olaf in disguise), Aunt Josephine says that the children will make them a meal of puttanesca. You need the stove to make puttanesca but Aunt Josephine would never let the children anywhere near the stove because she was terrified that it would burst into flames.
Continuity mistake: In the scene where the Baudelaires and Aunt Josephine are looking in the photo album, Violet turns a page. You can see the photo Aunt Josephine does not want the orphans to see, but when Violet turns to the next page, the same photo is there. (00:49:10)
Count Olaf: I must say, you're a gloomy looking bunch. Why are you so glum?
Klaus Baudelaire: Our parents just died.
Count Olaf: [nonchalantly.] Ah, yes. How very dreadful. Wait, let me do that one more time. Give me the line again while it's fresh in my mind.
Klaus Baudelaire: Our parents just died?
[Olaf pretends to be shocked.].
More trivia for Lemony Snicket's A Series of Unfortunate Events
Question: As we know, the magnifying glass in Olaf's tower started the Baudelaire fire. This is the same tool that Klaus uses to burn up the marriage certificate. If the magnifying glass was powerful enough to cause the Baudelaire mansion to burst into flames, which was 37 blocks away, why didn't the stage burst into flames as well?
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Answer: A magnifying glass concentrates all the light that goes through it at its focal point, and it is this focal point that needs to be placed on the object which one wants to set on fire. The distance of the focal point to the lens depends on the magnifying glass characteristics, and it is more than likely that Count Olaf chose a glass where the focal point would be situated exactly "37 blocks" away from his house, that is, at the Baudelaire's mansion. When trying to set on fire an object much, much closer, the glass would concentrate much, much less energy, and would only be able to set on fire easily burnt objects, such as thin paper.
AnthonyA