Yep, we watched that one too. She did realize it was pretty cheesy but still enjoyed it. She thought "Justice" was crap, too. So far Data is her favorite, and is fairly annoyed by Deanna, mostly by her wardrobe.
It's been fun so far, although when she points out mistakes or sloppy writing it usually goes like this:
Her: "Why did they/didn't they _______?"
Me: "I..uh...I don't know."