So I just finished my re-watch of S2.
I've said a lot about the pros/cons already in this thread. Ultimately, I'd conclude one absolute pro and one absolute con that I think summarize my feelings on the season as a whole.
PRO: They did a much better job of letting the characters out for some fun and development than S1. While I liked all the characters in S1, the circumstances of war and landing in a horrific and terrifying parallel universe didn't allow for much levity or chit-chat to be explored. It's just the nature of the situation they were in. S2 allowed for a lot more of this, and I think that was very good because not only is that a big part of the appeal of the franchise (for me), but it also leverages one of the greatest strengths of this show, which is the cast. The cast are all great, and the characters are all pretty well-drawn. This show should be leveraging the shit out of that.
CON: This comes down to one very simple thing: I think they tried WAY too hard. I think the writers and producers all had their hearts in the right place. I really, sincerely do. So it's hard to be "mad" or fault them for what they did. But, in the end, I think they just over-reacted to some of the criticisms of S1, and they really went over-board on everything in S2. For example, the amount of drama, anguish, emotion, and pain they put the Burnham character through is almost insane. People joke about SMG crying in every episode. I can tell you....having "binge" watched it (over 2 weeks as opposed to 14 weeks), she is in emotional agony....A LOT. I also mentioned how many plot points they decided to work with in S2 at some point earlier in this post. It was really too much. It made the season far too dense and it was hard to give any one of these items the time and development it may have deserved. It just felt like every episode was absolutely crammed with plot and dialogue and just "stuff happening" and there was hardly ever a moment to just breath and appreciate (or properly develop) what was happening and why.
I honestly think they'd be better served scaling back in S3. Tell a smaller, more fascinating story. Every show doesn't need to be Game of Thrones, and quality does not equate with complexity. Slow down a little. Let this fantastic cast shine. Don't save the multiverse, galaxy, or Federation. Don't be so self-conscious and just be a good show ("Don't try to be a great show. Just be a show. Let history make it's judgement."). All the pieces you need are there to hit it out of the park. Just relax and tell a great story, and don't worry about how much detail, complexity, action, and fan service you can cram into 13 episodes.
Overall, (unpopular opinion warning), I liked S1 better than S2. I think S1 was different and unique and, even when flawed, carved something of an identity that I found fascinating. S2 was a little less so, and I find that I missed that.
That's my story...looking forward to S3!