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.
Revealing mistake: When Violet and Klaus make the tent inside their bedroom in Count Olaf's house, they set up the light with the faces of their parents on it in front of it. Except when it shows the shadow of the object outside the tent, the edge of the picture frame isn't showing when it should. (00:21:40)
Klaus Baudelaire: Did Ike die in a fire?
Aunt Josephine: No, silly child. He was eaten by leeches.
More trivia for Lemony Snicket's A Series of Unfortunate Events
Question: Where were the children when the house was burning?
Chosen answer: On the beach, where Mr. Poe comes to inform them of the fire as the movie starts.