Poor story, feels like GTA with bullet time
Regardless of the new location or the new look, what was truly missing was the complex story, witty humor and smart story telling. The one-liner monologues of Max, and his constant self-pitying remarks are nothing similar to what was created in the first two games - I have a feeling the dialogue writers tried to create monologues and metaphors similar to the one in 1&2, but simply lacked the culture and depth to make that, and instead ended up with a blabbering drunk with repeating remarks that made no sense...
To sum it up, I think (and fans of the series may agree) it's eye-candy with a shallow story, and feels like a GTA with a character who happens to be named Max Payne
It is also linked very little to the previous developments: what of Bravura ? On the TV news, in Woden's manor they said he was stabilized after the shots. Max now had evidence that Winterson was at the construction site to kill him ( Winterson's message on Vlad's phone in Vodka club ), that Vlad was out to kill Woden ( Vlad's message on Woden's phone ) and that Mona was a lead in the case explaining the aiding of a fugitive.
All the above make for evidence that would have allowed him to drop the charges, and stay in the force perhaps even with a hero status.
As for the killing of the mob son - let's face it, he killed Punchinello and his entire goons before, and at that point he didn't have Woden's backing. Plus, given the attack on the police station by the Russian mob guys, the police should have embarked on a full fledged attach on all mob factions - meaning Max would have still had protection if he had remained in the force considering the above arguments.
To conclude, I think they could have done a better job with the story, and even though the gameplay is interesting ( though frustrating at times because of the amount of bullets it takes to kill even unarmoured thugs ), the story and feel of the original 2 is completely lost.
For me this is not a true Max Payne game, but a bullet-time GTA...