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).
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 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.