I think the only major problem with Gangplank that can be directly traced to the champion himself is his bonus gold generation, and I think his Plunder should just limit itself to Silver Serpents. As for the rest of his kit, I think the main problems actually come from the game systems it's tied to, rather than his own abilities: the mastery system complicates balance on a whole slew of champions without really providing that much gameplay of its own (e.g. Bandit giving GP even more of an income advantage, and Grasp of the Undying giving him too much poke before that), and I think we're at a point where it might just be better to get rid of it entirely. Crit is a system that should have been overhauled with the Marksman Update in order to be non-random, and I think that still needs to happen in the future so that Gangplank's power can stop being such a coin flip in a competitive setting.
To an extent, I think Riot is aware of this too, and doesn't want to really touch Gangplank that much because they're committed to preserving as much of his pre-rework identity as they can. Plunder is definitely something they should adjust soon, but beyond that I hope they rework crit in a subsequent update, and remove masteries in Preseason 7, both of which would go towards "fixing" Gangplank, along with many other champions and aspects of the game, without taking away from his quirks. There are probably some gameplay tweaks he could use beyond that (his barrels could be made simpler for both him and his opponent, and could probably also use a bit more counterplay versus melee champions), but in spite of his current issues, his current kit is mostly pretty healthy.