The following are Special Adventures and the earliest unlock points for them. Please note that a given Special Adventure is still beholden to the rules that govern their surfacing in game: you can only have one Special Adventure at a time and the Adventure you receive may vary depending on which Adventures you have in your queue of unlocked Adventures.
Special Adventures
Teacher Appreciation: Complete Year 2, Chapter 3 and not in Year 7
The Weird Sisters: complete Year 2, Chapter 4
Hosting the Beauxbatons: complete Year 2, Chapter 5
Meet the Malfoys: complete Year 2, Chapter 5, resurfaces at Year 3, Chapter 7 complete
Lone Wolf (Chiara): complete Year 2, Chapter 5, resurface attempt at Year 2, Chapter 8 complete
Sphinx Club: have a club level of 5 and complete Year 3, Chapter 1
Dragon Club: have a club level of 5 and complete Year 3, Chapter 1
Hippogriff Club: have a club level of 5 and complete Year 3, Chapter 1
Flume's Clues Chocolate Frog Hunt: Year 3, Chapter 1
Become an Animagus: complete Year 3, Chapter 3
Frog Choir: complete Year 3, Chapter 4
The Butterscotch Bandit: complete Year 3, Chapter 7
Meet Me At Godric's Hollow: complete Year 3, Chapter 7
Flying Solo (Talbott): complete Animagus special adventure, complete Year 3, Chapter 8
Expectro Patronum!: complete Year 4, Chapter 1
Mirror of Erised: complete Year 4, Chapter 2
The Celestial Ball: complete Year 4, Chapter 4
Creatures Everywhere: complete Year 4, Chapter 7
First Date: complete Year 4, Chapter 7
Party at the Weasleys: complete Year 4, Chapter 9
Become a Prefect: complete Year 4, Chapter 11
Grand Prankters: complete Year 4, Chapter 16
Forbidden Forrest: complete Year 4, Chapter 16
Valentine's Day: complete Year 4, Chapter 16, will resurface on Year 5, Chapter 7 complete
The Trials of Sir Cadogan: complete Year 5, Chapter 3
Clubs Tournament: complete Year 5, Chapter 3 and have the Club Secret Room unlocked
Romance Festival: complete Year 5, Chapter 5, will resurface on Year 5, Chapter 17 complete
The All Wizard Tournament: complete Year 5, Chapter 7
Valentine's Day #2: compelte Year 5, Chapter 9
Enchanted Kiss: complete Year 5, Chapter 12
Ticket to Love: complete Year 5, Chapter 12
The Quibbler: complete Year 5, Chapter 14
The Great Hogwarts Cookoff: complete Year 5, Chapter 18
O.W.L.s: complete Year 5, Chapter 24
Portrait Panic: complete Year 5, Chapter 30
Gringotts and Dragons: complete Year 6, Chapter 5
Cursebreaker: complete Year 6, Chapter 6
Head Kid: complete Year 6, Chapter 25
Seasonal Special Adventures (these only surface during the month of October for Hallowe'en adventures, or during December for Christmas adventures)
The Hallowe'en Feast
Howling Hallowe'en
Duelling Death Days
Halloween Curse (Godric's Hollow)
Christmas at Hogwarts
Christmas with the Weasleys
Gift of Gratitude
Holiday at Hogwarts
Quidditch Special Adventures (occur during the Quidditch season)
Comet: complete Quidditch Season 1, Chapter 8
Season 1 House Cup: complete Quidditch Season 1, Chapter 11
Respect, Rivalry, and Rath: complete Quidditch Season 2, Chapter 8
Season 2 House Cup: complete Quidditch Season 2, Chapter 11
The Legendary Snitch of Hogsmeade: complete Quidditch Season 3, Chapter 8
Season 3 House Cup: complete Quidditch Season 3, Chapter 11