The most relevant criticism of the U.S. military's Arabic language training would not, I think, be the quantity or quality of Arabic-language students, but rather a decision made a long before the first Gulf War about what language to teach them. Rather than learning one of the various regional colloquial versions of Arabic, students were only taught Modern Standard Arabic. From a linguistic point of view, that's roughly like teaching people Latin and then sending them to duty stations in France, Italy, Spain, and Portugal.
I was once told by someone at DLI that they used to teach several different "colloquials", but found that the various military branches were not able to keep the differences straight, and would assign someone who had learned Moroccan Arabic to the gulf, or vice versa, so that DLI gave up and went with MSA alone, since that's the standard written form which students need to learn anyhow. According to the website of the DLI's Middle Eastern Schools, they now once again teach Levantine, Egyptian, and Iraqi "dialects", "in the third semester of instruction, after students have gained a solid foundation in MSA".
Mark Liberman on Language Log