Continuity mistake: When the train is passing right in front of the car the train signal to the right of the screen is on with a red light. When it cuts the light is suddenly off. It would never have been turned off until the last car of the train had passed. (00:27:00)
Continuity mistake: When Violet and Klaus are setting the table for dinner we can see a chair right next to the edge of the table (on the opposite side of the rehearsing room). But when Violet and Klaus are done setting the table and Violet places the cup of cutlery on the table, the chair has been moved and can't be seen. When it cuts the chair is back. (00:17:20)
Continuity mistake: When Violet is telling about that time when their parents had written a long letter that got lost in the mail, her ponytail hangs behind her right ear. When it cuts, it's over her ear. (00:20:50)
Continuity mistake: Right before Sunny bites Count Olaf after the Baudelaires have made dinner there is a shot where Klaus says "No" to Olaf. When it cuts, Olaf's hand has suddenly appeared out of nowhere beside Klaus' head. (00:18:40)
Continuity mistake: Before the play when the man with the arm prostheses takes care of coats he is handed over a coat on his right hook and a hat on his left hook. When it cuts the coat is on his left hook and the hat is gone. (01:12:00)
Continuity mistake: As Violet approach the closet where the anchor is hanging she has her right hand up by her waist. When it cuts, it's down. (01:01:05)
Continuity mistake: When the Baudelaires arrives at the Curdled Cave and Aunt Josephine says "You deciphered the clues in my note" she is holding both hands over the edge of the rock on which she is lying. When it cuts only one of her hands are over the edge. (01:04:35)
Continuity mistake: As Violet and Klaus are looking over the edge of the broken house notice the broken planks. In the next shot the planks have changed. Some are shorter, some are longer. Definitely a different stage of scenery. (01:00:45)
Continuity mistake: When Mr. Poe is bringing the kids back from Monty, it cuts to a close-up shot inside the car of his hands on each side of the steering wheel. In the next shot his left hand is suddenly on top of the steering wheel. (00:45:20)
Continuity mistake: When Aunt Josephine hands over the photo album to Violet she hands it over with one hand. When it cuts she is holding it with both hands. (00:48:45)
Continuity mistake: When Count Olaf is driving the kids back from the custody hearing and the shot cuts from Olaf to the kids when Violet says, "Pure evil," Sunny is leaning against Violet, looking as if she is about to fall asleep. When the shot cuts back to Olaf, Sunny is sitting straight up and alert in between her siblings.
Continuity mistake: After Uncle Monty explains why they're going to Peru, he pulls back his jacket and puts his hands in his pockets, revealing the spyglass. In the next shot, his hands are behind his back, not in his pockets.
Continuity mistake: When Klaus throws the stick for Sunny to catch with her teeth he is holding a book with his left hand. His grip on the book change between the shots. (00:13:50)
Continuity mistake: When the Baudelaires arrive at Uncle Monty's and Monty says "We have to pack all the equipment" he has a snake whose head is over his shoulder. As Monty close the door it cuts and the snake's head is suddenly hanging down by his waist. (00:29:50)
Continuity mistake: When Count Olaf leaves the car on the train tracks and heads for the shop while locking the car doors with his remote, you can see that the mannequin's stop sign in its hand is pointing to the left. But when it cuts to Olaf hitting the sign it is pointing towards the camera. (00:22:55)
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.