I recently played through the game again, and it is a brilliant game.
It's just very fun, and the story is brilliant and interesting. Not only do I like how it tied to actual murders in LA, such as Elizabeth and the Dahlia, but the story behind the arson I also find to be really good, with the more and more cases you do, the more you find out about the suburban redevelopment fund.
Also Cole Phelps is just a really good character.
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It is a cool concept done poorly. For example, when you think someone is telling the truth and they are not, the game tells you they are lying. It makes it impossible to get thrown off and the game just holds your hand along the way. That plus the predictable plot (Obviously neither of these two guys are guilty of the crime, but I have to convict one anyway. Surprise surprise it wasn't them). The pointless freeroam that consisted of tons of driving and the terrible city events which were boring shootouts, each one exactly the same as the last. The whole detective thing is a great concept and I think if explored more could produce great games, but LA Noir fell short