"Superman doesn't kill." Yes! (Pumps fist in the air) Take that, Snyder! Although we did get a bit of gratuitous skyscraper destruction later -- but Supergirl at least bothered to save the civilians she put in danger.
I'm not sure I follow Alex's logic here. "Kara, you need to rest up after being exposed to kryptonite. Come back in the morning and we'll test your recovery by sparring in a room full of kryptonite radiation." Huh? Is this some sort of hair-of-the-dog thing? (Hopefully J'ank J'enshaw won't keep his identity secret from Kara too much longer. Those two could spar at full strength.)
So that's Non, huh? Much more articulate than the original version from Superman II. And let's see, by the current view of Kryptonian naming conventions, Astra's full name would be Astra Non. Sounds like a prescription medication. Or a rehab program for stargazing addicts.
Not sure I like the implication that Non is a bigger big bad than Astra. Sidelining a female character in favor of a more powerful male seems inconsistent with this show's usual approach. Hopefully all is not as it seems.
So Cat figured it out, and pretty quickly, too. One wonders why she didn't figure out that her coworker Clark Kent was Superman. Perhaps she didn't work as closely with him. Actually, for a moment, I thought she was going to look straight at Kara with glasses off and not recognize her as Supergirl. Her manner, as well as her hair, is different in Kara mode -- maybe not as different as Christopher Reeve's Clark and Superman, but more different than George Reeves's or Dean Cain's, certainly.
The cliffhanger was a little weak. It just sort of stopped in the middle of the big battle, rather than at a real moment of climax or imminent danger. A cliffhanger shouldn't just be "Now the fight begins," it should be a moment where the villains have gained the advantage and all seems lost.