Revealing mistake: In the scene where the children are first driven to Count Olaf's house, they turn round to see the house in the distance and while the house is fairly realistic the surrounding scenery and background are obviously matte paintings. (00:08:15)

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)
Chosen answer: The spy glasses are not explained in the books, but it seems that these are symbols of the fact that they are in VFD, the secret organization we learn about later on in the series. Both Dr. Montgomery and Aunt Josephine's husband and brother-in-law, the Anwhistle brothers, are implied to have been a part of VFD.