I can't add a lot to the other reviews, but I too thought it was an excellent movie. I missed the beginning (on a television movie channel), so I had no idea who was murdering who, except that the atrocities were happening in the former Yugoslavia. But that actually strengthened the message, that the primary victims of the war were civilians, not the armed combatants, who were often much more murderers of civilians than soldiers. I also didn't know the reason for Dennis Quaid's alienation, just that he was angry and miserable. My initial impression was that he was the baby's savior (and had tried to be Natasa Ninkovic's savior also). But other comments here point out that the baby was his savior as well -- from his own misery and alienation. He and the baby saved each other
The acting and directing were first-rate. The scenic photography was excellent too, but sometimes the tight budget showed, particularly in the sound quality. Still, the technical quality was generally quite good. The mix of English, subtitled local languages, and untranslated local languages was quite effective -- subtitles were used where they helped tell the story, but left out where the American's non-comprehension was the main point.
In spite of the mildly optimistic ending (which I found appropriate), it was a very gloomy movie. But it's such a good movie that you should see it, when you're in the mood for a very sad story.