If I were appealing a jury verdict, I'd sure try and make something of the fact that one juror showed up in a Star Trek uniform and believed herself a member of an organization on par with the military/Starfleet...
You could, I suppose, try to make an argument for inadequate counsel, but that would probably be your only way in on that one. Wouldn't be available to you if you were counsel in the case . . .
I suppose it could be useful in a case for malpractice against your own counsel.