First-time viewers might not catch this, but remember the part where Sophie travels back in time and she yells at Howl to "find her in the future?" Remember what Howl's first line to her is?
Howl: I've been looking everywhere for you.
In the book, the antagonist Miss Angorian claims to be engaged to Wizard Suliman. Similarly, the movie's antagonist is named Madame Suliman. So really, Miyazaki's choice to give that character that particular name was pretty clever.
In the book, Sophie has two younger sisters, Lettie and Martha. In the movie there's only Lettie, but a girl named Martha is mentioned at the beginning of the movie. While Sophie is watching Howl's castle from her window, the shop girls can be heard gossiping about a girl named Martha who had her heart "torn out" by Howl. Later, after Sophie becomes cursed and goes out into the Wastes, the man warning her of the danger says to his wife that she "says she's looking for her youngest sister".
Why does Calcifer like to eat everything? Because he's fire! And fire consumes everything!
In the book, when a duelist comes to ask for something to give him an equal chance in a duel, Sophie tells the powder she gives him that it will "make it a fair fight". Since she can talk life into things, it probably really did make it a fair fight!