The Austere Academy: Part One - S2-E1
Trivia: Mr. Poe rhapsodizes over a saccharine sweet book called 'The Pony Party.' That was the title of the fake book printed on the reverse of the dust jacket of 'Lemony Snicket: An Unauthorized Autobiography.'
The Hostile Hospital: Part Two - S2-E8
Trivia: When Olaf catches Klaus in the corridor while Klaus and Sunny are disguised as a doctor, he tells Klaus that he looks terribly young to be a doctor. This is a reference to the fact that Neil Patrick Harris, who plays Count Olaf, played the role of Doogie Howser, a teenage doctor, in "Doogie Howser: MD" in the late 80s to early 90s.
The Carnivorous Carnival: Part One - S2-E9
Trivia: When the orphans are disguised as freaks, Olaf and his troupe mock them by chanting 'Not one of us!' This is a homage to the 1932 film 'Freaks', where the freaks chant 'One of us!'.
The Austere Academy: Part Two - S2-E2
Trivia: While locked in the freezer, Larry recites the Jack London story, 'To Build a Fire'. Appropriately enough, this is about a man who freezes to death.
The Vile Village: Part One - S2-E5
Trivia: Mr. Poe suggests the villagers will draw lots to decide who will take care of the children 'Like in that delightful Shirley Jackson story.' He's referring to 'The Lottery', where the winner of the drawing is unceremoniously stoned to death.
The Carnivorous Carnival: Part One - S2-E9
Trivia: At one point, Esme asks Olaf why Madame Lulu is working at a carnival, and suggests she could "have a TV show in the city" if she were a real fortune teller. Olaf then casually mentions that he tried that for "nine years," but it didn't work out for him. This is a very subtle nod to the series "How I Met Your Mother," which was set in New York City and ran for nine seasons. Neil Patrick Harris, whom plays Olaf, was one of the co-stars of "HIMYM" from 2005-2014.
The Hostile Hospital: Part Two - S2-E8
Trivia: Right before Klaus is to perform surgery on Violet, a diagram is pulled down showing an anatomical view of a head, including the brain. If you look closely at the portions of the face that are visible, the head is actually Barry Sonnenfeld - whom produced and co-directed this series, in addition to co-producing the prior 2004 film adaptation.