The movie, Catching Fire, was missing several scenes that I thought were very important in the book. Personally, I believe that the movie should have showed the flashback of Haymitch winning his games by throwing an ax into the forcefield in order to defeat his final enemy. This part of the book directly foreshadows the way Katniss shoots the arrow into the forcefield, sending an electric shock through the entire arena in order to end the 3rd Quarter Quell and begin a revolution. After finishing the book the reader learns that Plutarch Heavensbee was behind the revolution all along, and he tried to warn Katniss of the "clock" at the Capitol's victory ceremony. Katniss does not realize that this was a hint until after she had figured out that the arena was actually one big clock. In the movie, however, Plutarch Heavensbee is much more clear in why he became head gamemaker, and there is no mention of the clock whatsoever.
Another major scene missing from the movie was when Katniss goes hunting and meets Bonnie and Twill in the woods. They are runaways from District 8, in search of District 13, which they believe to still exist even though it is said to be deserted. Katniss gives Bonnie and Twill some food, while the two try to convince her that there are survivors in District 13. After Katniss leaves the two women, she finds that the fence surrounding District 12 is charged again and she will be electrocuted if she tries to climb through like she normally does. Once she finally finds her way around, the new Peacekeepers are waiting for her at her home, very suspicious of where she has been. Katniss assures them that she was not in the woods and proves it with the stuff she bought for her mother and Prim at the hob. This scene is important in the book because it informs the reader that there are signs of District 13 and Katniss starts to believe it herself.
Of course there are many other minor difference between the book and the movie, such as Gale getting beaten for attacking a peacekeeper rather than for hunting illegally. The movie is not shown from Katniss' point of view so the viewers are not inside of her head all the time like in the book. Not all details of the book can be fit into the short amount of time in which a movie is shown. I do think that the movie resembled the book as much as possible and it showed most of the significant parts of the book in order to prepare the viewer for the third movie, Mockingjay.