That's cool they introduced the idea that sometimes Supergirl is going to have to fight human criminals with advanced weaponry. I liked that she had to figure out how to beat Reactron, although I didn't think they needed to go so far as to say Superman never could beat him (and he even failed to when he came to Supergirl's rescue). I'm sure Reactron escaping once would've been enough, although I did like Superman text congratulating her at the end. Guess that's one way of having them interact without showing him onscreen.
I like Kara having a crush on James and this episode showed how they're still feeling each other out, but her sister saying she's never seen Kara this happy around a guy before rang a bit false. It's still early.
Sheesh, how many headquarters with a team of people assisting her does Supergirl need? I don't think that room at CatCo is all that safe just because people are hesitant to go into an office where someone died.
I'd like to see a younger female hero look up to Supergirl and try to follow her example. Use someone like Wonder Girl or Mary Marvel...or maybe Ms. Martian would be easier and tie better into the alien thing.
I kind of liked the slip up, it can easily come out in a tense situation like that.
Don't forget an opening narration that establishes what the outside world thinks of them and then what they do/who they are secretly.