It's not clear yet whether Supergirl will be renewed for a second season. It would be a real shame if the involved parties couldn't come to an agreement.
Balancing those shortcomings, though, are some amazing performances and a whole lot of old-fashioned fun. Melissa Benoist is incredible in the lead role, making the portrayal of a Kara/Supergirl dual life seem effortless. She and Chyler Leigh have great chemistry as the Danvers sisters, David Harewood is an excellent J'onn J'onzz, and even Calista Flockhart's Cat Grant was growing on me by the end of the season. The vast majority of the show is relentlessly upbeat, with Supergirl refusing to be anything but optimistic in the face of any situation.
Supergirl started with pretty good ratings, but dropped significantly over the course of the season. That's true of many first seasons, of course, but in this case I think the problems I mentioned above made it worse. Those sinking ratings mean that CBS is thinking hard before bringing the show back for a second season. According to The Wrap, CBS is paying around $3 million per episode to Warner Brothers Television, which is a whole lot for a show with that downward rating slope.
The best solution would be for CBS and Warner Brothers to work something out to deal with the high cost. There are rumors that perhaps moving production north would help, for instance. They need to find some better direction in the plot pacing and writing areas, also. If they can't find a solution, maybe it would be possible to move the show to the CW, which already has Arrow and The Flash. Neither of those shows is perfect, but both are miles ahead of Supergirl in the writing area, so perhaps the production teams could help one another. Even if a network move means some major changes to the cast and/or setting of the show, it would be much preferable to a non-renewal.
In any event, I hope the networks can figure something out to allow Supergirl to continue. There were some outstanding acting performances in the first season, and the consistently upbeat and cheerful attitude is great. I'd love to see that continue, wherever it happens.