I saw the movie, then read this article; funny enough, my girlfriend and I had said quite a few of the exact same things that Bob did.
I guess I missed the implication in Basterds that the Americans were unwilling to bomb the church he was in, though.
When talking about what the movie did wrong, I kept referring to Indiana Jones -- there are a ton of things that the two Nazi-related movies in the series did significantly better than Monuments Men. This movie keeps trying to hammer home that we should hate the Nazis for destroying art, but then they undermine that by telling us to get mad about the mass killings. Bob Balaban's character finds the frame of a burned Picasso just as the other characters find a barrel of gold teeth; my anger at the latter act is going to diminish my anger at the former. As Bob pointed out, basically the same thing happens with the officer at the end.
Meanwhile in Indiana Jones and the Last Crusade, Donovan has the line talking about how the valuables (which the Sultan turns down in favor of the Rolls Royce) were "donated" by German families; the movie assumed you could figure out where those items came from. In the main plots of the two movies, it's perfectly sufficient to be upset that the Nazis are trying to steal the Ark and the Grail, because the viewer knows what kind of evil they want to subject the world to with that power.
Monuments Men keeps asking the question "Is art worth dying for and killing for?", but then it dilutes the message by pointing out even better reasons why we should fight, and risk dying. If we've then decided that we're fighting to prevent those deaths, how much can we really claim we're still fighting for the art?