Okay, a few more things to note:
According to ThatSRB2DUDE all the Specials from the first game are gone. That means no Kraken, Ink Strike, Bomb Rush etc., so Specials aren't limited to a certain power, except that they probably won't dominate the game or be completely useless.
In a similar manner, I believe that the Sub weapons have been changed too - maybe not classics like the Splat Bomb, but less iconic ones like the Seekers, Inkmines and Beakons don't make any appearances in the trailer (although what could be a new Inkmine texture is used for a Special), and the bouncing ink puck seems like a replacement rather than accompaniment for the Seeker.
Main Weapons seem to be similar, but some of those may be gone too to make room for the new ones - I'd say that some or all Blasters, Sloshers and maybe Brushes might be lost (ouch because I main Octobrush and second Luna Blaster Deco). If those appear in the trailer, please correct me.
Some maps have come in from the original game - Moray Towers is clearly visible, but also changed fairly drastically, so I think it's safe to say that the balance is very different in the new game, thanks to the weapons, hazards and mobility options available (jetpack Special and skinny laser of doom, I'm looking at you), so old maps will probably play very differently.
Other maps which I think could make a return are Walleye Warehouse as the Final Destination of Splatoon; Museum D'alphosino but increased in size because that was something that wasn't possible on the Wii U and the devs might have seen it as unfinished business; Port Mackerel as it seems to be a fan favorite, but possibly heavily edited to avoid a power imbalance caused by the jetpack Special - the easiest way I can see to do that is with inkrails; and possibly Saltspray Rig as a nice casual Turf Wars map.
Maps that I don't think will return are Bluefin Depot (largely hated for different reasons in Turf Wars and Ranked), Kelp Dome (only two levels, with one level limiting movement speed, so the laser of death would probably be OP), and Camp Triggerfish (nobody's favorite map from what I can tell, and the chargers got a buff which could upset the balance). Again, correct me if I'm wrong.
The map appears on pressing X rather than being on the Gamepad screen (I think it's a toggle? Maybe there's an option for that), and SuperJumps work by bringing the map up and pressing a D-pad arrow. The down arrow is for spawn, while the others are for each teammate, which means that 4 players is still the max for a team.
There seems to be more variety in the citizens of Inkopolis (if we even still start from there, maybe it's a new location). I saw another Shrimp and a kid Sea Urchin in the trailer, but there's probably more. The shrimp's ice cream shop is possibly a Sub ability changer of some description, as ThatSRB2DUDE pointed out the 3 ice lollies on the chalkboard, but I think they could relate to the 3 pieces of clothing that an Inkling can equip (or is that 4 now, with the pants?).
I won't go much into the story mode, but I'm surprised not to see Callie, and a little worried. Team Marie all the way but please don't kill the secondary waifu. The Octolings definitely make a return though, which is nice I guess.
Super Mario Odyssey was revealed and is an open-world sandbox, much like 64 and Sunshine, and seems to be on an epic scale. It looks amazing and has been very well-received AFAIK - important because it gives people another reason to buy the Switch, and thus more potential Splatoon players. However, it comes out very late (holiday 2017, which I assume means winter holiday), which limits the number of players at Splatoon 2's summer launch.
On the other hand, Legend of Zelda: Breath of the Wild is one of the confirmed launch titles, while Mario Kart 8 Deluxe, Binding of Isaac: Afterbirth+, and Sonic MANIA are all scheduled before Splatoon 2, along with a bunch of other third-party titles - this all means that there should be no shortage of players by Splatoon 2's launch. Afterwards, we have things like Pokemon Stars, Xenoblade 2, Sonic Project 2017 and again Super Mario Odyssey, which should ensure survivability for the rest of 2017.
Here's a list of confirmed titles for the Switch: http://www.eurogamer.net/articles/2017-01-13-nintendo-switch-games-confirmed-list-launch-titles
And I didn't mean for this to be so long, so I'll wrap it up. Overall, I think Splatoon 2 has a lot of potential, as does the Switch in general. Just be careful of the status quo changing, and remember that I don't exactly have a degree when it comes to this kind of thing.