Better story, characters, plot, writing. Also some focus.
A bit harsh, but the character and story writing have always been weak in the Golden Sun games. This was true in the GBA games and especially true Dark Dawn. That's the biggest criticism I hear from people who didn't enjoy the games,too.
Though the overall plot in Golden Sun 1 & 2 was not particularly bad, I kind of have to agree with this statement. The characters could definitely use more depth, in terms of personality--especially some of the characters in Dark Dawn. To mine memory, there was not a lot of character growth in any of the games. That is why I like Amiti so much; because compared to the other characters, he had a much more noticeable change in personality throughout his journey with Matthew and crew. Due to his sheltered upbringing, in the beginning he has a rather binary viewpoint on the world--this is particularly shown when he first meets Eoleo and his dad, Briggs; he is absolutely opposed to helping Eoleo at all and generally acts hostile toward him, believing that all pirates are filthy scumbags. But after witnessing the heroic acts of Briggs and working with Eoleo, Amiti begins to become much more open-minded and less judgmental. Also, Tyrell seriously needs a hard blow to his ego. Karis was pretty cool; I liked how she generally acted as the brains of the group and kept everyone in line. I hope they give her even more grit in the next game, assuming it gets made. I would have liked Reif better if he was less passive and a little more gutsy and forthright, and more of a wise-cracking know-it-all. [Shrugs] But that is just me.
In Golden Sun 4, they could not only give the characters more depth, but also build upon their relationships with each other. For instance, they could create scenes throughout the game in which the party is just taking a breather, whether at an inn or around a campfire. In those scenes, the characters could take their time interacting with each other and getting to know each other better. In this regard, I think Camelot could learn a lot from NamcoBandai's Tales games.
I'd also like an overhauled combat system. There are a ton of neat ideas there, but it doesn't come together that well. Dark Dawn felt too easy and having the same combat four games in a row will feel stale.
Personally, I am hoping they will keep the turn-based combat, but add a lot more things to it besides Attack, Psynergy, Djinn, and Summons. The monsters could be a lot smarter, and have special abilities to make up for their weaknesses. For instance, the bats could have very weak defence and HP, but could make up for that with extreme speed and various stat-affecting moves (e.g. temporarily immobilising the player with a piercing screech, or dizzying the player by rapidly circling around him/her (inducing the "delusion" effect)). In the GBA games as well as Dark Dawn, the boss battles were pretty fun because they required a lot of strategy and critical thinking to defeat (especially the Star Magician), while regular battles could easily become a drag, as all they really required was brute force. I remember posting a "Dark Mode" idea somewhere in this thread, which some users approved of. I could think of many more ideas, but in the end I would really just be wasting mine time, since they would never reach Camelot's ears.