So I just finished my first sitting of Heavy Rain, about 4 hours of it, and I'm not sure how I feel about it as a game.  As an experience, it is amazing.  The story telling is exhilarating and engrossing in a way that games as a medium rarely reach.  From the beginning I was caught up in the world.  The interaction with the environment and with the other characters in the world made you care about what was going on around you.  
The other story heavy game that came to mind after playing this is Mass Effect 2.  Vastly different games, taking wildly different approaches to presenting the story to the player, but operating on the same level in different genres.  Both make you care about the surrounding cast, both pulling you in with story in and out of cut scenes.  Both give you a feeling of urgency to getting through to see what happens. 
As a game though, Heavy Rain has some issues.  The controls are very intrusive to the experience.  Moving around the world is a hassle, with controls that remind me of Resident Evil for the PS1.  Its not as much of an issue when you are in some of the more open spaces, but when you are moving around a smaller environment, like some of the houses, you cant help but run into walls, or go in and out of the same room trying to get to a specific spot.  
I've also run into game crashing bugs.  The most notable happened when trying to turn around on a stair case, which sent me walking through the 2nd floor, then the roof and into the sky, unable to stop, and forcing a reboot.  Small bugs I can tolerate, they are an unfortunate part of gaming.  But bugs that crash the game are not really acceptable. 
I haven't had an issue with the quick time events.  The motion controls have all worked for me without any problems, though they take some getting use to being that you don't really see them much in games.  I think it does a good job adding to the tension of the moments and drawing you in more to the drama. 
As a story and an experience Heavy Rain shines.  It drew me in from the start and I had to force myself to stop to get some sleep.  As a game it has some issues, some small, some huge.  But the issues don't stop it from being a game that sucks you in and keeps you enthralled from the start.

I'm with you on this. I haven't completed a play though just yet. I don't know how far along I am and won't reveal anything for obvious spoiler issues. I am however, not convinced that Heavy Rain is anything special at all. Is it a game or does it just want to be a film you have some influence over? By some influence, I mean that it's obvious that your choices alter the story, but whether you actually have choice is debatable. You use Mass Effect 2 as an example, heavily involving story but one thing that games triumphs in is clarity. You always know whether your choice is a paragon or renegade choice, in Heavy Rain you simply don't. You get a spinning circle of vague choices, you never know if you will get them all or just one the game doesn't tell you anything.
 
Moving around the environments with R2 pressed to move forward is a strange choice as well, why have that? There doesn't seem to be a reason and I constantly find myself walking on the spot because some small item is blocking my movement. The controls for a game that is effectively made up of QTE events (just like Shen Mue) are an oddity as well. Who on earth thought that making a game of finger twister was a good idea? You find yourself with a desperately cramped hand struggling to move your finger to press that last button with four other buttons firmly pressed already.
 
Heavy Rain will be defended heavily because it's an exclusive and I personally enjoyed Fahrenheit, but Heavy Rain just doesn't feel like a game to me.

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KTHX