It's hardly news that you shouldn't file briefs with AI-hallucinated cases. But should you check all of your opponent's citations to see if they're hallucinated, so that you can alert the court to that?
I at first thought not. Naturally, if a citation is critical to the opponent's argument, you'll want to read the case the opponent is citing, and alert the court if the case doesn't actually exist. But many citations are on tangential points, cited for uncontroversial matters; there isn't much reason to try to track them down.
Indeed, even using a tool such as Westlaw's document analysis tool, which can do a good job checking citations in bulk takes at least some time and therefore client money: One needs to not just run the tool but closely analyze any errors it claims to find. And then one would have to spent time and money confirming that they are genuine errors and not typos, since one doesn't want to seem to be making a mountain out of a molehill, and writing up the analysis.