eleven gets more developed as a character, her vocabulary has actually improved since november of 1983 after all the time that she'd been living with hopper and it allows to show off how she feels and what she does with verbal reasoning to back it up
the head of hawkins lab is actually someone you can relate to for his goals, how human he is, what he cares for and how he goes about attempting to create leniency though the government is obviously forcing him to keep the kids, teens and adults who were involved with the upside down incident from talking to much
more hopper
more steve
more mike
more everyone else
focuses more on the development of lucas when he was just that kid in the group in season 1 that was there for the sake of being there and creating an opposition to mike's fondness and protection of eleven - this time it's actually shown what he cares for, how he's grown to protect eleven since 1983
returns to the woman who turns out to be eleven's mother, and shows what happens to her and how brenner covered up a mess that he created and blamed it on her experience with drug testing with lsd
steve actually turns into a more likable character this time, and it shows how he has some things in common when it comes to the younger kids - he's not some rich kid picking on jonathan this season; instead he's mixed in with the kids (dustin at first, the rest later) at the scrapyard when fighting the demon dogs and exploring the tunnels underneath hawkins with them all
hawkins lab is shown in a greater scape this time, showing how little the government are able to contain the upside down entrance in the lower levels when the lab inevitably turns into a murder space; the additional violence this season is most evident here, and a good payoff when it's shown - though this also plays in a different turn, showing how dr. owens differs greatly from brenner when he's willing to stay behind to save bob and guide the group inside to safety
hopper is shown with some vulnerability. he was one of the strongest characters in the show already, though this season cemented it to show his past, what he cared for, how he's unwilling to move on completely since his daughter's death and the extent that he's willing to go to if it can protect the kids, the teens and the adults alike. also a vietnam veteran if you read the boxes when it shows under the floorboards of his house
the ending twenty or so minutes where everything has been 'resolved' was paced much greater when compared to the ending christmas celebration sequence of the first season - much more enjoyable to watch and gives you a few smiles.
jonathan is fleshed out more and finally gets with nancy and feels it is his obligation to strike out against the government for what they have done to his brother and the pain him, will and joyce have to go through because of it. nancy also has her own motivations, such as the fact that the signing of documentation after 1983 forced her to have to continue a lie with barbara's parents about the fact that their daughter wasn't dead, though she of course she knows barbara is dead after eleven went in the upside down in hawkins high school and told the group
there's three or so 'main' stories running at once, with numerous semi-stories/events going on at the same time (dustin and lucas' attempts to get with max, hopper protecting eleven as best he can, mike attempting to communicate with eleven via radio in his basement, nancy and jonathan teaming up with murray to send out their recorded tape when brought to hawkins lab, eleven investigating her past, max and billy's domestic issues, et cetera). though it's all molded in a perfect and unique way so that one of the events will affect the other, which helps resolve another and brings characters together (most clear in episode 8 when steve and the kids follow the demon dog to hawkins lab, where they meet nancy and jonathan, where they meet hopper, joyce, will, mike and bob, where they escape to the byers household and create their plan of action for the climactic ending in the final episode) this was a nice break from the sluggish feel of season 1 at some points where it felt the only thing happening was joyce attempting to contact will in the upside down, with nothing else going on to keep the viewer entertained and other things.