I wonder what they'll do for the inevitable sequel.
They will probably go the safe route because people love what's already there.
Obviously they can introduce new weapon types, etc...
Maybe an expanded singleplayer.
Not that I expect these things but improvements I could see made for the sequel:
Expanded Single-player- a more robust adventure that builds on the creativity and ideas seen in the original single player. It should also build the world a little more and flesh it out. Inkopolis and the single player aspect felt bare bones. Perhaps they could incorporate the secret mission tunnels into an actual city. Inkopolis could be a large city/island, they could incorporate different missions all around the island and also finding the hidden secret underground passages. The center of the city would be the same plaza as in the original.
Multiplayer:
Local Multiplayer- should be a priority! If Splatoon had local multiplayer it'd probably be an even bigger success that it has been. It's harder for word of mouth to grow when you can't really play local multiplayer/coop on it. It also would somewhat alleviate people's frustration of not being able to play certain maps when they want to.
4 maps every 3 hour rotations. Allow you to bring two load outs(preselected clothing and weapon combo) without having to leave the lobby. Have the lobby be a bit similar to the MK8 lobby. Allow you to view other inkling's load outs and order stuff while there. Also can use some pretty selected Splatoon Emojis/sayings(similar to Triforce Heroes). Or you can just play one of those minigames while you wait. Also since they are going to more than likely go the no VC route, it'd be nice to have more phrases than cmon and booyah.
Ranked mode could share the same map rotations as turf battle but allow you to vote on which mode to play it on(or have 3 available at a time). Include the original 3 modes and introduce 3 new ones.
As for map count, I'd say 25 maps total but launching with 10 maps and 4 modes. Have 9 of the maps return from the original Splatoon. I'm curious about Ancho-V Games and how it will turn out because I'd be somewhat interested in more stage specific gimmicks like this and in Mahi Mahi Resort.
There should also be someway to allow others to play the game without them having to use your character/save. It's hard to get people interested in the game when anytime they play they are forced to use my character who is at a high level and high ranking which means they get annihilated on multiplayer and don't enjoy it as much.
Playable characters:
Inkling further customization options(hair styles?), ink colors, pant customization, etc.
Perhaps other playable characters. They could introduce different playable sea creature/human species like Inkling and Octoling. They could offer four different species playable that offer slightly different stats and abilities than Inklings.