At the beginning of the film, there are parallel scenes; Karras visiting his mother in her apartment, and Chris putting Regan to bed. Both mothers are warm and nurturing, and perceive their kids as each having something on their minds that they don't fully reveal.
The scene in the book where Dennings gives Regan a birthday party on the set, rewarming the lights to film her cutting her cake — he calls it a screen test, and promises to make her a star. This can literally bring tears to your eyes knowing what's about to happen to Dennings.
The film equivalent of this is a deleted scene in which Chris takes Regan on a tour around Washington D.C. for Regan's birthday. The scene is a bit darker as well, as it reportedly involves Regan asking her mother why people have to die while at a soldiers funeral. This scene was to be restored into the film in the 2000 rerelease, but the soundtrack became lost.
During the Exorcism, Father Merrin treats the girl very gently. He still knows that in the body is the little girl, trapped and held hostage by the demon.
At the end of the movie Regan McNeil hugging and kissing the priest on the cheek after seeing his collar. Especially since it comes right after we have been told she doesn't remember anything of her ordeal. In the book, and the film stage directions, she has a "sudden remembrance of forgotten concern." Blair's expression is perfect.
After a bit of Nightmare Fuel where Sharon shows the "Help Me." mark to Karras, the next scene immediately has Karras request to his higher ups permission to perform an exorcism. This is a man who was in the middle of a Crisis of Faith. A man who intended to treat Regan no different than any psychiatric patient. (He's also a shrink.) But when he finally realizes that this is no psychosis, he is willing to do all he can to save the girl. Especially at the cost of his own life.
It's an easy one to miss but while preparing for the exorcism, Regan's mother asks Father Merrin if he would like some brandy. He looks to her and says "My doctors tell me I shouldn't, but thank God my will is weak." And he accepts her hospitality.