His relationship with Marceline had amazing potential to grow as Finn grew but the show totally stopped caring, and better stuff could've been done with Flame Princess as well.
Those are my main concerns and what I think needed to be fixed the most. Other stuff like the Flame Princess breakup arc could definitely be improved as well but I don't think those were as high a priority. Finn's arc was rocky as fuck and the show really did spend too much time shoving his face into the mud and in general being weirdly harsh to him which didn't feel deserved, especially since most of the worst shit he did felt out of character in the first place. The writers were making a Finn strawman be an asshole then spending tons of episodes chastising him and making him be sad about his assholeness.
Unlike a lot of people on /co/ I think his 'maturation,' while overly hyped (people don't seem to care much if Finn is interesting only if he's mature, it's real fucking weird) was done well enough for me to be alright with it. I did like how in the later seasons there were times where he clearly had a better handle on stuff than in the past like when it came to not sperging out over girls or being able to handle situations without bloodshed. Also unlike /co/ I didn't think his maturation made him boring since he always felt like he had that spark of life in him except for some of the show's lowest points.
I love Finn a lot as a character and the show did not treat him completely right which is sad. I wish the finale at least gave him a good note to end on but he got benched for half of it which was frustrating as hell. If he didn't give PB the finger and go against her there really wouldn't have been anything satisfying for his character at all which is very very sad. But I still love him despite the show's best efforts.