The Reptile Room: Part Two - S1-E4
Continuity mistake: Count Olaf enters the bedroom with a knife and says "Oh orphans! [Beat.] Our ship awaits." A few minutes later when we see the same event from another direction, there's no pause, and the delivery is noticeably different, more "oh orphans, our ship awaits." (00:19:45 - 00:23:20)
The Wide Window: Part Two - S1-E6
Continuity mistake: The sticker of the smoked mackerel that Lemony Snicket places on the weather chart completely changes position between shots.
The Bad Beginning: Part One - S1-E1
Continuity mistake: During Count Olaf and his theatre troupe's performance in the front hall, the bannister and the newel post wobble when Count Olaf grabs it.
The Wide Window: Part One - S1-E5
Continuity mistake: When the Baudelaires are having dinner after Josephine leaves, Sunny is seen placing her rattle into her bowl. In the following shot, she is holding her rattle next to the bowl.
The Bad Beginning: Part Two - S1-E2
Continuity mistake: When Olaf is standing at that secretary's desk, he reads the calendar and says his name is "haircut." The secretary and the top of her desk are shown several times and in most of the shots, the calendar is visible near the secretary's left arm. However, in at least one of those shots, the calendar vanishes.
The Reptile Room: Part Two - S1-E4
Continuity mistake: When "Stefano" puts his ankle up on the table, in the brief closeup his sock is pulled up straight. In the wider shot it's noticeably rumpled. (00:31:05)
Continuity mistake: When the Baudelaires are on the rickety trolley with Justice Strauss, they pass the pebble that Violet drew an X on near the start of the episode. The shape and thickness of the X change each time the pebble is shown.