Well, I have so far 5 hours of gaming with Max right now. Pre- and after first patch.
The single player portion has a lot of concerns for it being in bright favela land Brazil - but to me - they make the story pretty OK - all things considered. It's a hard boiled game with a washed out Max, nothing new and the new Max would be the most sought after mass murderer ever from the scores you kill - but they are all bad guys - promise ;)
The biggest issue with Max payne 3 isn't the story, the washed out Max, the loss of the cold city streets or even the shaved head Max - it's the game itself and the mechanics.

The game plays like this - all the time:
Starting with flashing and creepy graphic styles with stutterings and words being highlighted graphicly from Max's monolouge. People are talking in the background and Max answers sometimes and more MTV effects. You are lead to an action point and fter three or four minutes intro - you are then released into shooting down some targets - they die and hopefully you don't empty your stash of painkillers. The shooting lasts a few minutes - you are ready to storm on - but no - more cutscenes comes into effect - you get loss of your preferred weapons and your sight - you are guided to shooting gallery 2,3,4 or however long the sequence is - your sights gone, your weapons switched this time - you are inches away from enemies - all who know where you are - and action.
Once in awhile that's OK - but it is all the bloody time. I have the scrollwheel for switching weapon setup (1 handed, dual wield or 2 handed guns like AK's, shotguns etc). Oh, and if you like the AK47 - don't go into duel wielding since then the 2 handed AK will be dropped to the floor and Max will draw his other guns. I can't really care to tell you how many times this killed me in tight situations. Really frustrating.
But I got over it, using the 1, 2, 3 and 4 keys to select guns with. The cut scenes leaving you with other guns and sight off? It got better after the patch since the sluggish aim got better - but they break the gaming rhythm to play the story. The story is fine - but not stellar so I would have preferred much more game time.

Another problem with cut scenes shooting galleries is that the game feels really really like a linear shooter. You are following a red line that doesn't let you deviate much and since your partner or some other low life good for nothing dude is around to stress you into the right area - you are also feeling like Max has a noose-ring that you are being yanked around with.

The movement of Max is painful as usually - he dives and shootdodges in slow mo etc - but the free sight and movement isn't really working all that nice. It is easy to loose your aim simply since the little white dot gets lost in all the now so bright colours - something the original games didn't have as a problem. The various setups for aiming isn't helping much.

When you do get to do some fighting and running around a bit more "freely" the game is really fun - but it is far too seldom.

The MP part is the SP part done fun. A bit hard to steer your character and with a bit too many problems of how the things work and not. It's a learning curve and the all too apparent flirt with the modern form factor of levels, lock up load outs, weapons and of course the different customisation of your character. Well - I think that the game-play is pretty fun and fast and the few maps are so far action oriented and pretty fun.

All in all the game is rather fun - but not stellar - it is really fun at the best of times and tedious and a bit booring when at its worst...

Hopefully patches and add ons will iron out some more of the flaws - but the biggest issue is so much a part of the game.