Though reviving a property as iconic as Rod Serling's "The Twilight Zone" was always going to fall short of expectations in a certain sense, Jordan Peele's first slate of episodes came up shorter than even most people thought. It generated enough interest to garner a second season, however, and here can be seen a clear increase in overall storytelling and quality. Though I still wouldn't rate this in the upper echelon of current TV fare, I certainly didn't struggle with it like I did the preceding campaign.
The biggest change from S1 to S2 was the overall tone or genre of each episode. Season one featured episodes that tackled heady social issues with the barest of sci-fi premise to fulfill the TZ mantra. Here, each episode is much more mystery or science fiction themed across the board (with the social commentary woven into those main plots). Personal tastes may comprise one's overall ranking of these styles, of course, but I very much preferred this new style of episodes.
One oddity I experienced while watching S2: the first four episodes underwhelmed me. Again, still better than S1, but I sort of got that "here we go again" feeling in terms of overall quality potentially lacking. But then, almost every episode from the mid-point on really captured my interest in at least some way. Well, until the finale, which (unfortunately) is a bit too weird/outlandish to really drive home the message on a solid theme. So, if you aren't "feeling it" after a few episodes, give S2 a little bit more time and it might pay off for you.
Overall, it was nice to see this show improve from its freshman slate of episodes. I think there is still a lot of room for improvement for the writers to continue figuring out how to adapt Serling's unique style for a modern audience, but progress is definitely being made. I'd surely watch another round of episodes should one be forthcoming.