Supergirl

Haven't watched this since the first couple episodes, but I do have them all recorded. Did this pick up and turn out to be a good show?

Obviously I'm going to be watching the flash crossover episode, but are the rest worthwhile and should I try to catch up first?

I like that they had fun with the episode at least, even if the villains were pretty terrible. Flash was awesome like always, but some of the comments were golden. My favorite was the part where Cat told them they looked like the pretty young multicultural cast of a cheap CW show (or something like that). They were even kind of posing, as if for a photo shoot, while she said it. Also, Wynn having a bro-out with Barry was great. Only thing dumb was Jimmy getting jealous of him, but it was part of that storyline they were pushing so whatever.

I know the show is cheesy at times, and like any superhero show they have things that defy explanation (not superpower-wise, but I'm talking things like how 3 of her employees manage to disappear for hours at a time, constantly), but to answer the question above, I've really come to enjoy this show. It isn't high cinema, but it is light enough without being silly, which really came to the forefront this week after watching the grimdark BvS movie and realizing how terrible that is for certain characters. Supergirl is fun, Flash is fun, and together they were even more fun. I hope she comes over to their world soon because I *really* want Cisco to a) tell her he could come up with a better name, and b) have a crush on her.

I really like that Melissa clearly had a good time with the episode as well. I love her reaction here:
(after much trial and tribulation, it seems I can't embed gfycat anymore, which Fedor has made abundantly clear)

Flash treats supergirl to ice cream - Gfycat

Yeah, not really sure where you are getting the low production values thing from, but maybe something just struck you wrong in the two episodes you watched. It isn't amazing, but none of these shows are due to budgetary restraints, and considering her powers and the powers of many of the villains and other characters, they do a decent job. You're certainly welcome to not like or watch the show, but two episodes isn't really enough to judge the entire show on.

EDIT: That's in response to Homsar, not Tenks.