There were some great moments in season 2, especially any involving Q and Picard being a sage advisor to others, but overall the writing was really poor when it comes to plot holes, interweaving plot threads, and character stupidity. Ramblings...
When Seven got re-borged, I howled at her getting the exact same implants in the exact same places to fix a stomach injury. That was beyond stupid, and really pointless since she was going to be re-borged once they fixed the timeline anyways.
Seven and Raffi spent the entire time in the 21st century bickering and being generally annoying.
The FBI guy was a totally pointless, wasted character considering the actor who played him was Ducane in Voyager, a literal Federation time cop.
Tallin's ability to control people remotely without them knowing gets totally ignored after Picard finds her, which would have been useful as hell in several situations.
Tallin looks exactly like Laris and is also Romulan because reasons. Kore looks exactly like Soji because reasons. Spiner is fine, that's established tradition for him to be every Soong ever.
Rios and Jurati were great, as was the Borg Queen, doc Teresa, and the new actress they got to play Young Guinan.
Special Ops borg were ridiculous. They're borg, therefore they absolutely must have green lasers to give away their location and targets at all times.
Butterflies are super important except when they're not and casually ignored. Escaped deported immigrants. Borg special ops all dying. The guy Borg Queen Jurati killed after fucking up the bar. Rios staying behind (they could have at least asked Q if that wouldn't screw everything up), etc.
Picard's story with his childhood and his mom were good plot ideas, but handled really poorly by stretching them out and over-complicating it way too much. If they had kept it to two dedicated episodes, start to finish, it would have been perfect. Also, where the hell was his asshole brother when all this stuff went down? Lost story opportunity there that would have played into his long time resentment for Jean Luc.
How the hell did doc Teresa know how to use a 24th century medical device to help Picard? That's like giving a laptop to one of the pilgrims and saying "you got this".
Q's final moments really got me in the feels.
Wesley shows up and recruits Kore to join the Travelers because reasons.
Lots of ups and downs.