I've played the game for a good amount now and there are some problems that I (like many) would like addressed:
AI - I mean, come on PD. GT6 has the least ambitious AI racers ever. I've played Midnight Club LA, NFS Shift, TDU2, NFSU2, NFS Carbon, Cars the Game, and a whole flock of other racing games, and honestly, GT6's AI is right down there. They never deviate from their own lines, and even slow down to let you win. What the hey? Let me race against the likes of someone like Gan-san from Best Motoring.
Drivetrain modelling - Needs work. Gearboxes for example don't behave the same way their real life counterparts would. There is also some questionable torque steer (though absent on DS3s, I found on the G27 wheel). Front wheel drives though, definitely need some help. No hints of lift-off oversteer. Oh, and clutch modelling, really needs work. Using the H-shifter on wheels is a much harder task than it should be.
Tires - Not in the sense of their modelling, but more in terms of what tires stock cars should be equipped with. I shouldn't have to test each tire grade to see which one can pull the most realistic numbers on the cars.
Sounds - I'll give PD the benefit of the doubt. I really hope it's improved in the future.
Wheels - Wheel users have very limited options for settings, and more so for G25/G27 owners. Added to that, the FFB needs major work. The wheel just doesn't give us enough feedback. As an example, on rFactor, decelerating the car, whereby the weight of the car shifts to the front, you can feel the steering wheel jolt in response to that. No such thing in GT6.
Damage - I don't care for visual damage, but mechanical damage is pathetic. No engine damage (e.g. inability to blow up engines), no transmission damage, no brake fade, no damage from burning the clutch. Yeah, pretty bad.
Water - No hydroplaning. Enough said.
Next are related to gameplay.
SRF - I understand the need to cater to the casual gamers, but at least give us the option to turn off SRF. It's really annoying since all Special Events and Licence Tests have them forced on. What the hey?
Career mode - While GT6's career mode might have qualified as such back in 1997, the fact is that it is very lacking when compared to its contemporaries. While GT Mode does a good job bringing a sense of familiarity to GT-fans, something new is needed. A career mode like that in Codie's F1 series is a good start.
Invalidated laps - It would make sense for this if there's a global leaderboard, but there just isn't. So why the need for it? At least let us turn it off.
Leaderboard - I played GT3 recently, and I realized that GT3 could hold up to 16 (I believe) different times. Added to that, you could delete an individual time. In GT6, you can only have 10, and if you delete one, you delete all.
Garage menus - While GT6's menu is way faster than GT5s, I still prefer GT5s. In GT5, you didn't have to sort the menu every single time. It was fixed. In GT6, it isn't. I also miss the sub-menu after you choose a car.
Rolling starts - I've yet to find a race in GT6 that has standing starts. Rolling starts suck in GT6, period. For one, the cars are way too spread out. Because of this, races feel like what people call "chase the rabbit." If starts were closer together, and if the AI was fixed (lol), then rolling starts would be a very welcome feature. As of now though, no.
Auto drive - For God's sake PD, let us drive through the pits on our own, and let us do the formation laps on our own as well. I want it to be like in rFactor, where we had to literally drive from the garage. No auto-drive as far as I know.
I still play the game though.