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Dr. Strangelove
Paths of Glory
Full Metal Jacket
The Enemy Below
Catch 22
The Pianist
The Great Dictator

The last two might not involve military, but they are an excellent commentary on European society in the 40s
 
Meh. I didn't care for it. I thought it was shallow and special-effects driven.

Now that I've watched Threads, as recommended by jeremy h upthread and again featured in its entirety on YouTube, I find myself agreeing with you. Threads is quite grim indeed, and captures the pathos of the whole situation a bit more realistically than TDA.

I might have to check out your Testament recommendation.
 
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