The New York Times covers this in an interesting article (which quotes and links to this post of mine on the subject). I'm inclined to agree with Rod Smolla that the law is likely constitutional; and this argument from Ron Collins doesn't seem to me to work:

"If the government cannot under the First Amendment compel reverence when it comes to our nation's highest symbol [the flag]," asked Ronald K. L. Collins, a scholar at the First Amendment Center in Washington, "why then can it compel reverence when it comes to lesser forms of symbolic expression?"

The law here doesn't bar speech that lacks proper reverence — it bars false statements of fact (and should reasonably be interpreted as barring only knowingly or recklessly false statements of fact), and the Court has held that false statements of fact generally lacks constitutional value. Nonetheless, as I argued in my earlier post, the caselaw is not entirely clear on this.

UPDATE: Surreal typo in title ("medical of honor" instead of "medal of honor") fixed. D'oh! Must have seemed pretty confusing at first glance.