I still love the game and play it very often but there are lots of things they could improve.
Filter Battle Lounge results by region. I get the impression that they deliberately chose to omit this option to promote international matches, showing their confidence in the netcode but, even though it's a big improvement over the netcode of SFIV, it rarely works out when fighting players so far away.
A choice of intro/outro/taunt animations. Matchup-specific intros would also be great. They've sort of implied that some additional polish in this area may be coming with Arcade Edition.
Reduce Loading times. Right now I rarely return to training with Fight Request on because it's so much quicker to return to the main menu. Just switch my training mode to whichever stage I just fought on in ranked if it speeds things up.
Give normals to have more range. It can feel pretty frustrating so see a normal you were sure was in range whiff. It'd skew the balance since it'll likely make for rangier confirm combos than are currently possible, benefiting some characters more than others, but hopefully it can be done without reintroducing the jab, jab. jab confirms of SFIV.
Reward frame-perfect inputs somehow. Maybe perfect execution could be rewarded with extra hitstun so that confident players can execute links into moves which would otherwise be impossible. Even at lower levels of play you'll often see the same optimal combos experienced players use because the buffer negates difficulty. Opening up new combo routes for players willing to try for riskier links may make things more interesting.
Team Battles. I'd love 3x3 KoF style team battles. They added this to USFIV but I'd love to be able to play it with any number of players, between 2 and 6, online or off. Ranked Team Battles would be nice; grouped into a little party with two friends to fight another team of three, like SFxTekken had.
Improve Replays. I want to be able to watch replays without having to first save them to the replay list. I'd like the return of a replay theatre where replays which meet your search criteria (Diamond matches between Bison and Akuma for example) will play endlessly until you quit. Right now you have to pick up the controller after watching a single replay so you can't put it on in the background like SSFIV.
More Options. I'd like a set of "system direction" style dip-switch options; turning on things like infinite meter, universal parries, air blocking, Super Jumps, chip damage KOs etc for local or private online versus. Might be interesting to see how the game feels without its input buffer or with the risk of being chipped to death.
Improved Tutorial. A tutorial on a par with what the newest Guilty Gear games offer; not only teaching how to do moves but also how to recognise situations where these techniques are appropriate while testing understanding in practice.
Ideally I'd like a tutorial mode fused with a story/world tour mode; branching paths which take you through the game's mechanics, basics to advanced, universal to character/situation specific, with unlockables on route. It'd be more interesting to play than a standard Arcade Ladder.
Also this might be a PS4 issue but I'd prefer it if plugging in a controller and playing were more straightforward. It can be a pain when you have a group of friends all using different controllers/setups.
Character wise I'm not too fussed. My personal favourites would be Rufus, Dan, Makoto and Eagle. Playstyle-wise I'd like someone like Sagat or Gouken; more projectile keepaway play to diversify the cast.
I'm looking forward to seeing how Arcade Edition turns out.