Continuity mistake: In the scene where Count Olaf starts walking from the balcony to the stairs, you can see his right hand when he is saying "lovely home" with no writing. Later when he looks at his hand to remember Violet's name, his hand has writing on it. (00:09:20)
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)
Continuity mistake: When Count Olaf is welcoming the Baudelaires he reach out his hand for Violet and says "Enchante", and you can see his fingers are separated. When it cuts his fingers are clenched. (00:10:10)
Continuity mistake: When Uncle Monty is telling about the Incredible Deadly Viper and he says "My assistant Gustav and I may be the only people who ever seen it", as he stops by the cage he has his hands up. When it cuts his arms are hanging down. (00:31:00)
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.