Sophie:(to Madame Suliman) That is enough! Now I understand why Howl was so concerned about coming to see you! It's a trap! You lure people here with an invitation from the King and then you strip them of all their powers! Howl would never be so heartless! He may be selfish and cowardly and sometimes he's hard to understand, but his intentions are good! He just wants to be free! (starts to become younger) Howl won't come here. He doesn't need your help. He can fix his problem with his demon on his own. I'm certain of it!
Every time Howl uses his bird-form. Him using it to catch a bomb is probably one of the best.
During the climax of the movie, the town's being bombed, houses are on fire, and Sophie's obviously worried about Howl, who's in the thick of things. She then finds out that Suliman's henchmen (very creepy black goo-monsters) are trying to break into their flower shop. She meets them on the front steps and angrily tells them that instead of trying to catch Howl, they should do something useful, like putting out the fires.
Sophie standing up to Howl's wangst. First she tries to cheer him up, then she yells at him for being so whiny over his hair darkening, then calmly drags him upstairs to wash off the goo he summoned over himself. When Markl, obviously terrified of Howl's behavior, asks if he'll be okay, she tells him "It's fine. No one's ever died from throwing a tantrum."
The animation in general is superb, but come on, who would expect anything else from Studio Ghibli? The moving castle itself in particular is gorgeously drawn and animated. Seeing it on the big screen is a huge "Holy SHIT!" moment.
Any of the moments where Ingary's military forces are on their pre-deployment parades.
A meta fact is that this has a fairly unique standing within Studio Ghibli, and Japanese animation in general... The author that the material is based on is English, and it's a (reasonably) faithful adaptation.note There have been numerous Sherlock Holmes versions, among others, but they are heavily interpretive.