I'm about 3 hours in and I'm loving it so far. The game is awesome, though it does have a few flaws. Mainly you're never really given a break to explore around, it's one case after another. You can drive around whenever you want, but it feels odd you're exploring around and there's a corpse waiting for your inspection somewhere, i.e. you're always working on a case and you'll always have a partner with you, at least so far.
If you play the story straight through, though, the game really shines. There's a bit of guess work involved and it's all about the big feature, the faces. I completely botched the interview before I got promoted, I think I retried it 4 times, but I eventually got my head together and pulled it through. My biggest advice is to RTFM, you'll get a lot of clues there on how to properly play the game and how to best read people (hint: straight face look at you means they're telling the truth). Once you figure that out, it's more manageable and actually a lot more enjoyable.
On the Xbox 360 version, there are noticeable frame rate drops in some parts, namely in the opening sequence. Some of the graphics are also pixelated, taking you out of the experience, like the blood in the car in the first traffic case. The hair are also kind of funny looking, like they slapped a photo of the hair onto a mannequin. So a few little oddities like that here and there, but the overall presentation is very good. The city in particular looks stunning and it's huge.
Still a ways to go, I just wish I had like a free-roam break or something. Sometimes having mission marks scattered around the map is needed, like in RDR or GTAIV, but this game doesn't operate like that.