Let me state for the record that I love the addition of Batgirl to the cast. I’m the child of librarians, so I approve of a heroic character who is one (see also: Giles, Rupert; Carsen, Flynn), I like her cheeky attitude, and best of all I like her costume. It’s a small thing, but the red hair that sticks out from under her cowl is a brilliant bit of concealment, since hair color and style is one of the main things we use to identify people. I find it impossible to credit that anyone who sees both Bruce Wayne and Batman, and especially anyone who sees both Dick Grayson and Robin can miss that they’re one and the same, but I can buy it with Barbara Gordon and Batgirl.
So while I enjoy her introduction—especially the misdirect in thinking that she’s the helpless victim who needs the Dynamic Duo to rescue her, only to have the tables turned and she’s the one who rescues them—it’s just a pity that it has to happen in an episode that makes absolutely no sense.