Quite a bit. Having an older system for this game is likely an asset, especially if you have a single-core processor, since that's all the game uses. It barely uses GPUs; I'm sure that part of that was them gathering playdata from users (I'm not sure if they have a way to track performance but it would be smart if they did) to optimize for common GPUs and go from there. Either way, it will not launch running anything like it did during this beta. Very few of us could run it properly with even a few players on-screen.
Then there's balance. The scaling seems to tip from moderate to crazy insane raid situations very suddenly, and it also leads to problems like having masses of enemies spawning behind you out of nowhere if, for example, a big group enters a cave behind you. You're likely already dead by the time you figure out what the hell is going on.
PvP/WvW need massive tuning. Melee is basically not viable for DPS. I doubt Anet will ship the game in such a state. PvE has the same issue but much less so, especially once you figure out dodging (fewer players than expected seemed to from the grouping I did).
The personal stories are scaled oddly as well. It seems like human players mostly finished their run; I played Charr and I heard from several Norn players the same story: You can end up hitting a brick wall where the difficulty scales too high, your AI partners get wiped, and you have no chance of taking out anybody. And because of level scaling, you can't grind your way out of the situation, so it's purely a balancing issue, or perhaps mastering some aspects of the game that many of us didn't figure out yet.
Lastly, there's the glut of plain old unfinished content. We don't know the status of two of the races. Random scouts were not voiced at all. Various blatant glitches such as a skill point location that only becomes active after a server reset were all around the world. WvWvW has kind of off pacing where too much time is spent traveling, though that might be intentional.
Yeah, there is a hell of a lot to fix. And that's without really getting my hands dirty with specs and stats and skill issues.
As far as true betas go, though, I was incredibly impressed with the game. The uptime was actually pretty good for the first major stress test. Many MMOs have launched in far worse shape regarding that. Overflow works amazingly, except for the fixable issue of breaking up parties. Guild chat was up and down but by the end of the beta it was rock solid. And most importantly, the game is challenging and fun as hell, the first time I've played an MMO and actually found something beyond my expectations. An MMO focused on skill, that cuts out most of the boring bullshit, that rewards exploration and world PvE, that encourages working with absolute strangers, that provides a fair PvP environment... and I didn't even touch crafting yet!
This game is going to be amazing. But I'm not sure if June is possible.