It's improved from 2 or 3/10 show in the first season to about 5/10
I suspect the issue is that Mike McMahan had more creative freedom as the show progress while in the first season Alex Kurtzman had more say and influence (I suspect that he was responsible for the mean-spirited stuff in the first season)
To see how the show has improved. I summarise what I dislike about the first season
- the show prioritise jokes/humour (that are often unfunny) over suspension of disbelief. The balance that I believe the show should aim for is to have the show be funny while at the same time people still behave like people. Having bad jokes where people in a middle of a crisis and yet having two people socialising and engaged with their conversation in the first episode ignoring the crisis is an example of how they make people behave in an unrealistic manner for a sake of a joke.
- Utter mean-spirited bullying. There was a sense of Boimler who believed in the traditional Star Trek values and then being portrayed as the loser and be the butts of the jokes. I never get an impression that Boimler ever did anything bad to deserve his treatment. The show was essentially the jock bullying the nerd.
- Utter obnoxious behaviour from Ensign Marriner. She is portrayed as a character with poor impulse control, behave in a reckless manner and endangered the crew, completely disregard the chain of command etc. I wouldn't mind if the show has a character like that if this character was portrayed in a negative manner. However she was the hero and gets everything right at the end. Stuff like her using Batleth and swinging at Boimler and causing injury to him (ie. serious assault) was ignored with no consequence.
- Subtext that Marriner represents Nu-Trek, Boimler represents Classic Trek. Marriner is the hero and Boimler is the loser. There was a subtext of Star Trek is a nerdy show for loser and if you like it and also dislike the directions the show was heading to with Discovery/Picard then you are just like Mr. Boimler.
Second season actually re-
The turning point of the show was the episode "Kayshon, His Eyes Open". There was almost explicit message of Nu-Trek vs Old-Trek message - You have initially have members of the USS Titan engaging in action battle after battle. You have the crew member making fun of the old episode of Star Trek TNG where people were more preoccupied with poker games while they get to do cool stuff such as involve in action ship battles and dangerous away missions. You have Ensign Boimler struggling to deal with the transition from traditional Star Trek shows to action oriented nu-Trek. It just seems another let's bashed old trek again. However the end of the episode shocked me as they had Ensign Boimler passionately defended classic Trek stories to the other crew and ended up inspiring them to return to traditional Trek values and then the episode ends with Captain Riker and Boimler reminiscing about the Enterprise D.
After that episode Ensign Boimler was no longer the butt of the joke
Then later on in the series you have Marriner trying to fight the way out of trouble and gets captured. Then Ensign Boimler using diplomacy to convince the Ferengi to let them go and save the day "Mugato, Gumato". Another episode Boimler uses his intelligence to capture a dangerous AI while Marriner thought he was naive and falling for the trap "Where Pleasant Fountains Lie".
Marriner obnoxious behaviour was toned down. There was a scene where she drived like a maniac and nearly killed alot of people and the show just ignored it ("An Embarrassment of Dooplers") where the old awful Marriner from the first season was back. However outside that, for the most part she is far less irritating, her impulse control problems is tone down and she doesn't always solve the problem of the episode at the end.
Some of the jokes is actually funny there was an episode where a bridge crew-member who died in the early season going back to life. One of the lower deck character was shocked that they return to life. However the other member of the crew was like "bridge officers always come back from the dead" and treated it as nothing, Then the character was then speculating how exactly the person was coming back from the dead and started listing various coming back from the dead methods (genesis device, nexus, parallel universe etc)
Still though the show leans heavily on Member Berries of reference and nostalgia rather than being great independent story. Also Marriner is still annoying for me to really like the shows. However I can watch the show without being extremely annoyed which is an improvement.
It's easily the best out of the Nu-trek show (better than Discovery, Picard, movie-reboot)