I generally agree with what you wrote, even though I guess I enjoyed the movie more and didn't find its flaws as bad as you did. Still I can't agree with this one:

"Mann and his fellow screenwriters don't even seem to know what they want to say about Dillinger the man."

I think they knew what they wanted to say and what they wanted to say was "they, the gangsters, were just plain normal people, they were just living in crazy times". I wrote more about it in my reviews of "Public Enemies" here: http://michuk.filmaster.com/review/public-enemies-are-just-regular-fellows/

They were shallow, yes,. They were not even too smart, correct. So what else would you expect to see? Dillinger quoting Shakespeare? A universal tale about life an death?

My reception was that it was a greatly directed tale about last months of life of an accidental villain, who really wanted to "get away somewhere hot" with his girlfriend, but life lead him to different places instead.

I did not expect much more than a fine story and I definitely got it!