I have already argued that the Stolen Valor case is important because it breaks with the rigid methodology used in recent years by the Court to determine whether speech should be unprotected. See here. The case may be important in three other respects.
The Court sometimes says and some commentators maintain that public speech receives more protection than private speech. Yet in the Stolen Valor case, the reverse is the case, at least for the four justice plurality. The plurality maintains that public utterances falsely claiming the receipt of a medal of honor should be unprotected, but if the same statement is uttered in private, it should be protected. Yet, I would think that the statement uttered in public is less likely to cause damage because its falsity is more likely to be quickly discovered as were the facts in the case before the Court.
More disturbing is an aspect of the dissent. In a previous case, the Court ruled that an ordinance outlawing racist fighting words (a form of unprotected speech) was unconstitutional because it unreasonably outlawed some fighting words without outlawing others. From Justice Scalia's perspective, St. Paul Minnesota had taken a side in the culture wars. RAV v St. Paul. I do not agree with the result in RAV, but I think the equality principle upon which it relies is unassailable. For example, it would be obviously unconstitutional to outlaw fighting words directed against Republicans, but not against Democrats. It seems to me that the opinions in the Stolen Valor case certainly needed to discuss RAV. According to the statute it is not permissible to wrongly claim that you have earned the medal of honor, but it is permissible to falsely say that you once served in the Peace Corps, or as a lawyer in the Justice Department (when you are not even a lawyer) or as a Doctor in the Veterans Administration (when you are not a doctor). Surely this content discrimination required some discussion under RAV.
Finally, the Alito dissent argues that First Amendment interpretation has not depended on originalism. Yet Justice Scalia and Thomas, the apostles of originalism, sign this opinion. Perhaps Justice Scalia could claim that his originalism allows him to bow to precedent (though these bows are selective). I do not see how Justice Thomas could say this. Nor do I understand how Scalia could miss the need to discuss RAV. I am left to speculate that the rally around the military politics implemented in the law blinded Scalia and Thomas to the need to explain why they were not taking one side in the culture wars.