There are two main issues I had with this first episode of Supergirl:
Firstly, that she
[spoil]seems to be oblivious to the burgeoning animosity towards aliens[/spoil]
Although it is somewhat understandable (hope etc), it does imply that she has been ignoring things going on around her, or has been dismissive of them. One of the things she seemed to ignore was that [spoil]they took both spikes[/spoil].
The second was that
[spoil]she was slower than a couple of motorcycles[/spoil]
Unlike the first issue, I have no excuses for this one.
It was good to see Lillian Luthor again, and I grinned at the reveal of Otis and Mercy (like I've said elsewhere, I don't check on previews etc, so I rarely know about these things ahead of viewing).
Otis was certainly more capable than the version of the character made famous by Ned Beatty in Superman but there was still the recognisable clumsy and slightly goofy element to him. The actor playing him also reminded me of The Cowboy from Innerspace.
Separately: Winn was never J'onn's PA, nor was he ever Alex's, yet, for some reason, Alex seems to treat Brainy as if he is her PA. As Director, Alex would almost certainly have an assistant for the admin side of things. It may be that J'onn was someone who kept things closer to his chest and preferred to handle the paperwork/arrangements himself, but it's highly unlikely. It just doesn't fit with the idea of a government agency, regardless of how secretive it is.
As for the reveal, leading in to the season's initial arc, I think we knew it was only a matter of time before the secret that [spoil]President Marsdin (played by Lynda Carter (Wonder Woman)) is an alien[/spoil] would be uncovered, after we saw a flash of the truth last season.
As with previous seasons, there is a lot within the show that reflects what is currently going on the world, especially the US, and, while many don't like the approach, I think it's a good way of keeping things different to a number of other superhero-shows.