Rub this dandelion under your chin. If fuzz sticks on your chin, then you're in love!
Then you must not be in love.
It...doesn't stick, but I'm married!
The Sieve and the Sand
Scenes with Clarisse, specifically the interaction involving the dandelion is incredibly important, because she opens Montag's eyes to the truth of the world around them on his walks home from work. By making him more aware of nature and his surroundings, he starts to ponder his job, his marriage with Mildred, and his society as a whole.
It is essential to the plot that Montag asks Faber for help once steals the book from a house that he burns down. Faber helps him understand the meaning and gain knowledge that he was reading and being taught. From this point on, Montag would pursue self-education and tries to rid of the instilled ignorance.
Wow this is absolutely incredible! I'm going to learn so much from these books.
Montag's escape along the river away from the city was very important to the novel, because this scene allows him to reflect on the recent events. His reflections highlight how he was grown intellectually and gained some bit of wisdom as he starts his new life.
Granger, Montag, and the other professors and knowledge-holders continue walking along the river until they find the city of St. Louis, so Montag can meet up with Faber, as planned.
After arriving in the abandoned city of St. Louis, Montag searches for Faber, but instead stumbles upon a library with a large variety of books that fill all of the shelves in the building.
Faber finally arrives at St. Louis with a group of professors, but once he shows up, St. Louis is bombed; there are no survivors from this warfare.