New things I have noticed from my playthrough of the demo.

[Cephalobro]

First, Splatsville is the biggest and most complex lobby we will get yet, there's a combination of alleyways, big open spaces, and stairs that lead to some of the stores.

Eyebrows still match the character's gender, even with the same eyebrows having different looks depending on whether the character is male or female. The curved eyebrow option is longer for males than females for example.

Speaking of customization, the screen to customize your Inkling/Octoling with gear and weapons actually doesn't have any music, it's unknown at this point whether this is part of the final game or not.

Believe it or not, a track from Splatoon 1 can be heard in the training room, though, you won't actually get to use the room itself before the Splatfest.

 

[Elbowtross]

The equip screen not having music seems likely due to the fact that the lobby system has been overhauled and no longer has the traditional queue. Now it seems to just muffle the current ambiance of whatever area you're in. I think this is intentional and will carry over to the full game. As an aside the equip screen now loads in much faster than before I've noticed.