The only legitimate problem mine has had in its almost 50k miles was a faulty ignition lock cylinder (not the recalled switch we all know about). It failed shortly after the warranty expired which caused the key to be completely stuck in the run position! GM agreed to split the repair cost with me. I took advantage of the warranty while I had it for a few things that were mildly irritating; condensation in one headlight, slight rattle from the steering column, squeaky clutch pedal. I have only done a few modifications; software, downpipe, upgraded intake tubing, "rotated transmission mounts". My tune is conservative, but should still be good for around 300 whp. Believe it or not, the power is usable and torque steer isn't too bad at all. With a good custom tune that is tuned for the hardware upgrades (this is important), these engines shouldn't have any real issues other than eventually needing an intake valve cleaning, like any direct-injected motor.
I think these cars are an absolute riot to drive, yet still just comfortable enough to live with as a daily. The performance numbers are impressive even by today's standards, but the overall driving dynamics are also very good. Canyons or twisty back roads are the best places to be. They feel nothing like a base model and also quite different from the supercharged Cobalt. People always complain about the cheap interior. Yes, you're certainly surrounded by hard plastic! I think it was well designed/laid out though and the bits you actually touch while driving feel good. Someone in this thread mentioned a lack of lumbar support, there is a lumbar adjustment that's easy to miss on the front of the driver's seat (the passenger doesn't get one). Other than styling which is subjective, the only real gripes I would say are fair would be premature rear brake wear and lack of usable interior/cargo space. The trunk is big, but the opening is very small. Not very practical compared to a GTI or Speed3. If you can find a 2009-only turbo sedan (good luck!) it's not as bad. Any other shortcomings shouldn't be that surprising given the price these sold for when new.
You can pick one up for not a lot of cash these days, it is getting harder to find clean examples that haven't been abused though. It's incredibly cheap and easy to make huge power with the LNF engine, but because of that a lot of them have lived a hard life. It also doesn't help that many ended up in the hands of immature owners who didn't treat them very well. The RPD is nice, but LSD is the only option to really hold out for. Not difficult though since so few (roughly 20%) didn't get the optional limited-slip. It was only standard equipment on 2010 Canadian cars, in the States it was optional every year. If you can find one that's been well taken care of, it can be quite a performance bargain!