One of the most important differences between the book and the movie is the absence of a minor character, who has an important backstory with Katniss. My friend Kate Hicks, in discussing the film with me, actually had to point out this subtle but important difference. In the book, as Katniss is preparing for the games, she meets several individuals from the Capitol who serve her meals and drinks. One of those girls is an "Avox" (a mutilated servant) that Katniss remembers from earlier.
Katniss remembers the girl as someone who was trying to escape from the Capitol, but who was subsequently captured by the government. Labeled a traitor, her tongue was eventually removed. In the book, we learn the back story of this girl and how Katniss regrets not trying to save her when she had the chance. But in the movie, this relationship is never fully realized and Katniss' connection to this girl is never revealed.