Replaying the game now and having a blast. Probably my favourite game this gen. I've swung around aimlessly for countless hours. That said, there's a few things I think need to be improved for the sequel:
Web-swinging: It's fantastic, near-perfect, but I want to see the 2-trigger swing mechanics brought back. It makes things a little more immersive. The back-bone of any Spider-Man game, it can get deeper and more satisfying.
Combat: Like above, I really enjoy it. I do find I slump really easily into patterns though. A few attacks just work reliably and I get a bit sick of seeing them. More animations, more combos, more integration with web-gadgets.
Other playable characters: I like MJ a lot in this, the switch to reporter keeps her active and useful in the plot. This does not make her fun to play however. Miles fares no better. I quite like the perspective shift, but the novelty wears thin real fast with such paper-thin stealth segments. If Miles is playable next time he's sure to be much more interesting. As for MJ, if she has nothing better to do than sneak about and read stuff, hearing it in a line of dialogue will suffice.
Side-missions: These are mostly pretty weak in all honesty. Basic collectable hunts and challenges with a special guest radio host. This ought to be a lot more varied and imaginative, making use of Spidey's huge roster of characters. Some more involved 'cases' would be greatly appreciated, as Parker's life should always be packed and chaotic.
Random-crimes: A smaller element of the game, but one of the first essential details you spot in a game like this. I would love to see Insomniac delve more deeply into procedural generation and bring more life to the NY streets, with shifting tides of rival gangs fighting for turf across the city. Think nemesis system in Shadow of Mordor, but with low-level Spidey villains in place of orcs. You already take out strongholds in the game, how about giving them more impact in the game world.
DLC: This is an odd one, but if there must be paid dlc next time around, I hope it is better integrated into the game. 3 separate game worlds for 3 fairly short chapters of additional content is really lame. It requires a bunch of loading in-and-out of the same place, and only serves to hightlight how sparse the offerings are. I was really hoping that devs would patch in a "Play All" for the dlc so it felt a little more complete. Honestly, I think it would play better as side-quests in the main story anyway, barring a few things that would have to be end-game for continuity.