Private Reiben: You wouldn't shoot the kraut and now you're gonna shoot me?
Sergeant Horvath: He's better than you.
In the scene where the medic gets shot, watch the shot where Upham brings the bags up to the injured medic. The next shot there is some fog which then reveals the injured medic. In this shot, watch carefully as the cast rips away the medic's shirt. If you look near the neck, you can see the fake stomach vest he is wearing for a split second - when the actor realizes he ripped too far up, he quickly covers it back up.
The movie was shot in chronological order, which is unusual for a film. Spielberg chose to shoot it that way so that the actors would feel like they were going through the experience in the same order as the characters they play, and they lose friends on the way. This helped create the resentment towards Ryan, who doesn't share the journey with them.