I'm a believer that plots aren't that important, and nearly any plot could be interesting if it is executed well. So my "things I would do differently" are more general and about characters and execution.
1. They shouldn't have isolated Burnham so much from the rest of the characters. The show needs to have more character interactions among the regular cast. Character interactions are what makes a show fun and entertaining -- not watching one character fight through personal angsty moments like someone with a machete cutting through the deep-drama jungle. Too much of that is neither fun nor entertaining.
I get it that Burnham is the main character, and I have no problem with that; I like Burnham. However, since the action and the "camera" need to mostly follow the main character, write the story so that main character interacts with the rest of the characters more frequently. In that way, we can see the rest of the characters and see those (hopefully) fun and entertaining interactions between them.
I think this isolation of Burnham from the other characters is what rubs some people the wrong way and causes some to (inaccurately) label her as a Mary Sue. They have her doing so much for herself and by herself , and often without any support or input from the crew that it gives the appearance of being a "Mary Sue."
2. They need to put Tilly and Stamets together as a mentor-mentee pairing. They seem to feed well off of one another: Tilly with the lack of filter, and Stanets with the prickliness to tell her that her lack of filter can be annoying -- PLUS the warmth to be able to be brutally honest with her in a positive way.
3. More Saru. He is always good for a wise word, and he has the ability to look at situations from a thoughtful angle and verbalize that thoughtfulness. Saru could act as a secondary mentor to Tilly while Tilly is on the bridge. He, too has the ability to tell it like it is without sounding overly critical.
4. S-L-O-W D-O-W-N the pace. Take a few moments for the characters -- and the viewing audience -- to consider and reflect on the on-screen situation. Allowing the audience enough time to reflect on what's going on with the story makes for a more memorable story. Jumping quickly form scene to scene does not give the audience time to remember (long-term) each scene.
Slowing down the pace will also allow them to do a better jog tying up loose plot points. When they throw everything plus the kitchen sink at the action action, some plot points are bound to be missed. Basically slowing down would serve to tighten it up.
And if they are going to use quick-cut multiple-camera work in a scene, learn how to do it in a way that isn't so jarring.
I though the scenes on Terralysium in New Eden were technically well done; quietly and thoughtfully paced, but still carried the story along. However, in that same episode we had the constant break-neck running, fast camera cuts, people talking over each other, and generally frenetic scenes on the ship itself. That seem like a split-personality episode -- and I liked the slower-paced personality.
5. It seems they learned their lesson with ship design. The ships in season 1 (such as the Klingon ship and the Charon) were so amorphous and had too much going on for a person to take in that they may as well have looked like nothing. The audience should be able to have a mental picture in their mind when they think about the ships that were just presented to them. That was nearly impossible in season 1, but much better in season 2.
So I applaud them for cleaning up the "noisy and busy" ship designs in season 2. Hopefully that will continue in season 3 and beyond.
Archer has been Beckett in his descendants body the entire time!
