For many, many viewers, Molly's rant when she first meets the unicorn flew over their heads as kids. Coming back to it after having learned the mythology of unicorns, though, can break someone into tears quite quickly (as evidenced by its presence on the Tearjerker page).
A group of unicorns is called a blessing.
The book never makes it explicit, but Hagsgate "sharing Haggard's feast and sharing his fall" meant the unicorns. The townspeople didn't try to stop the Red Bull from driving the unicorns to Haggard because every time the Bull caught one they were able to see it pass through their town. Is it any surprise that the unicorns trampled Hagsgate on their way out?
The reason Haggard's land was so barren was because there were no unicorns to keep it verdant; they were all trapped in the sea.
The Harpy's cage was hardly sturdy. Just imagine her getting prematurely released and killing all the helpless people in the Midnight Carnival.
Actually, it was probably a perfectly good cage before the harpy started working her magic on it; by the time the unicorn came, the only thing keeping the cage together was Mommy Fortuna's magic and the fact that it was iron.
Also, Lir always talked to Molly and Schmendrick about his feelings for Amalthea, but he never told Amaltheaherself. It's a brilliant and utterly depressing instance of Fridge Horror, and it makes everything that much worse.
To be fair though, their duet and his Heroic Sacrifice to save her probably made that pretty clear. Actions speak louder than words, after all.
Much ado is made about turning Amalthea back into a unicorn which would make her incapable of loving Lir and being together with him since she would outlive but why does the option of turning her back into a human never come up. Turning Amalthea back into a unicorn when the characters couldnt be sure they could find the rest of the unicorns was understandable since theyd be no more unicorns in the world otherwise. But after the rest of the unicorns are rescued and Amalthea has been turned back into a unicorn, why doesnt Schmendrick try to turn her back into a human since Amalthea wanted to remain a human and only turned back to defeat the Red Bull and with unicorns back in the world its not like one less unicorn would be noticed. Perhaps it couldve been impossible or not but the point is, Schmendrick didnt even try.
The book seems to suggest that magic works on its own and only comes at times rather than Schmendrick having full control of it. Besides, the more time she passed as a human, it was suggested that she would forget her true identity completely. Even with all the unicorns back into the world, it would still be sad for her to forget herself.
"Amalthea" wanted to remain human, to remain "alive". The Unicorn only wished to find/free the other unicorns and then return home.