Surprised to see all the negative comments regarding the Catco stuff. Secret identity, news office, light-hearted tone is exactly what a lot of people want for Superman, yet when it's applied to Supergirl, now it's lame and just for teenage girls?...I'm curious what tone people wanted for a Supergirl show (granted I have never read a Supergirl comic).
Personally, I would have made it sillier, or darker, or more stylized, or some combination of those. Light-hearted is a broad description for tone, and there's a lot of nuance there, and I'm not feeling the particular vibe we've seen.
Some other things I'd do differently (that may or may not be generic guy answers):
1. If you're going to copy Superman and set it in the media, just have her be a reporter. Assistant = boring.
2. If there's going to be someone who doesn't believe she has what it takes in the media business, Lois & Clark had the right idea: have it be the romantic interest. It consolidates so that you're killing two birds with one stone, it creates dramatic tension, and it gives the romantic interest more of an identity than "the romantic interest".
3. Speaking of which, Lois in Lois & Clark was the feisty one, and that more striking personality (and her determination to uncover stories) helped her hold her own as a character when Superman was the one who was actually saving the day. Now, granted, none of us have seen the show, but in terms of what this trailer is selling...why should I care about Jimmy Olsen? Does he have a personality beyond generic nice guy? Goals? Secrets? I think Kara has the hots for him, and maybe straight women/gay men will, too, but I don't care. Then the other guy is Hulk who just wants to eat ice cream with Black Widow.
For those of you who don't get that reference: these are presumably the two biggest male characters, and with six minutes to work with they were presented as little more than romantic prospects. That isn't a sign that CBS is targeting male audiences.