Ok so to start a couple notes:
 
1) I was going to like this game.  Apart from controls just not working, Deadly Premonition level production issues, or an unplayable game, I was going to like this game.  And I do.  So that will color everything I say and have said about Bulletstorm.
2) I played five hours of the campaign last night.  I just met the general dude.  Don't know what percentage I'm done, don't know my pacing.  Could be half way in or 90%.  I'll probably find out tonight. 
3) I'll try to stay away from major spoilers, but in the context of Bulletstorm, I'm not sure there are major spoilers.  So watch out.
 
 
Ok, on to my impressions.  This game is meant for me.  When I play shooters these days, I get bored quickly and usually wish we could go back to what I liked about Unreal Tournament (My crazy shooter game of choice) or Soldier of Fortune (My game with a campaign guilty pleasure).  Compared to the demo, even, this game feels a little faster/smoother.  That's nice, makes this game less 'gears-y' and more it's own game (an admittedly old-school game).
 
Onto gameplay:
 
So as Jeff said, this game has some ammo conservation built into it that noone was expecting.  I haven't run in to this per-se, but there is a whole strategy to the way you spend skill points on upgrades.  The basic function here is that as you get skill points (which you get more for if you're creative with shooting/killing), you can use them at the dropships to buy more ammo, buy charge shots, or upgrade either.  As you come across new weapons you also have to spend an initial investment to unlock that new weapon in the dropshop interface.  Dudes drop ammo, so you don't always have to buy ammo, and most dudes use the assault rifle, so it's not too hard to work out which Gun you probably don't need to buy ammo for (but upgrading the ammo capacity helps because you have more reserves then).  
 
The game rewards you not getting bored and just plowing through dudes.  So, if I were to just use my rifle and shoot dudes, relying on careful aiming for headshots or just killing them, I wouldn't get alot of points, but I would make it through the game.  It rewards you for taking your time and pacing your kills.  Doing that, you get more time to work out environmental kills and use different weapons, getting more points in the process.  Also, there's a strategy to your weapon loadouts.  There are portions, for example, where a sniper rifle is almost required.  They give you a gun then.  You can switch you 2 secondary weapons with any guns you've unlocked at the dropshops, so depending on where you are in the unlocks and how you play, it makes sense to use specific loadouts.  For example, since I played the demo so much, the flail gun and the pistol are my best weapons for skill shots, so I use them alot (racking up skill points along the way, unlocking greater ammo storage for these guns and upgrading the guns i'm not using)
 
Ok so that's all to say there's more to the game than appears at first sight.  One could say the game is a crazy over-the-top shooter that gets pretty repetitive.  On the other hand, what I have observed is that you can certainly play the game this way, but you are rewarded more for 'strategizing' how you play the game.  Not only that, but the skillshot names are cool and seeing you screen fill up with skillshots is rewarding by itself.  That takes me to another point, the UI in this game is really good.  Not too busy, not too minimal, sort-of where I would want it to be.  
 
 
Level Design and Set Peices:
This game is crazy.  The world you get placed in is huge, and it seems like when you're not actively killing dudes, they're trying to show off what they've done with this world they've created.  That's cool and it looks amazing.  There are some amazing in-world events as a result of the story part of the game, and some crazy monsters/bosses you face.  This over-the-top part for me is really really satisfying.  As most of you have seen, the robot dinosaur part is super cool.  It was also challenging as the robot controls were flawed somewhat in the way you would expect them to be (which is the robot dinosaur shoots from it's head, so it's not so much like a big tank.
 
The language/voice acting:
This is what will probably be the most polarizing part.  I like that this game takes itself so un-seriously that the writing feels like it was done by a 13 year old or auto-generated.  The dialog (and story) is absolutely balls-to-the-wall batshit crazy.  And it's better for that.  I think some people look at this like the weakest point, but to do that I'd have to think this game was intended to be serious (a'la Cod, Halo, Gears, etc).  But it's not.  So I'm ok with that.
 
 
Actual Weakness:
The engine.  I like Unreal.  So I like this game, and the style.  It's not too gears-y, which is good because I don't really care for the gears unreal look.  However, Unreal has issues.  Texture pop-in comes up here and there (actually only once in the 5 hours I played and for a cutseen and 5 minutes of game play after that).  What happened was grey's character never loaded right and some of the in-world objects didn't load right either.  The game righted itself very quickly and I got over it.  But nobody likes that, and i hope if that one area is busted they fix it and if it was a random glitch it doesn't happen again.  Part of what I like about the unreal engine is the sizing of everything is more video-gamey and feels a little bit bigger.  People look like they're 7 feet tall, versus the normal height in CoD games and the five feet tall they feel like in Battlefield games.  I think this is a bit of a visual preference that people either will or won't like.  I do, but I can certainly see how it would turn people off.
 
 
Wrap-up:
In any case, this game will most likely be pretty polarizing.  I think the game itself is solid, and reviews and gamers in general will/should see that.  The tone of the game may come under fire (already has) as will the length and extra features.  I think this game is good enough that it coupled with DNF later this year can change the course (which I don't like) of like every AAA shooter to come out for a while now.  However, even if it's not a) I like this game, and b) I think it will end up like Red Dead Revolver.  The forgotten spiritual prequel to a game which later was absolutely amazing, and re-introduced a whole new genre to gamers, the western.  So in either case, this game is refreshingly old-school, and hopefully more new games will be old-school (and good) too.

Ok so to start a couple notes:
 
1) I was going to like this game.  Apart from controls just not working, Deadly Premonition level production issues, or an unplayable game, I was going to like this game.  And I do.  So that will color everything I say and have said about Bulletstorm.
2) I played five hours of the campaign last night.  I just met the general dude.  Don't know what percentage I'm done, don't know my pacing.  Could be half way in or 90%.  I'll probably find out tonight. 
3) I'll try to stay away from major spoilers, but in the context of Bulletstorm, I'm not sure there are major spoilers.  So watch out.
 
 
Ok, on to my impressions.  This game is meant for me.  When I play shooters these days, I get bored quickly and usually wish we could go back to what I liked about Unreal Tournament (My crazy shooter game of choice) or Soldier of Fortune (My game with a campaign guilty pleasure).  Compared to the demo, even, this game feels a little faster/smoother.  That's nice, makes this game less 'gears-y' and more it's own game (an admittedly old-school game).
 
Onto gameplay:
 
So as Jeff said, this game has some ammo conservation built into it that noone was expecting.  I haven't run in to this per-se, but there is a whole strategy to the way you spend skill points on upgrades.  The basic function here is that as you get skill points (which you get more for if you're creative with shooting/killing), you can use them at the dropships to buy more ammo, buy charge shots, or upgrade either.  As you come across new weapons you also have to spend an initial investment to unlock that new weapon in the dropshop interface.  Dudes drop ammo, so you don't always have to buy ammo, and most dudes use the assault rifle, so it's not too hard to work out which Gun you probably don't need to buy ammo for (but upgrading the ammo capacity helps because you have more reserves then).  
 
The game rewards you not getting bored and just plowing through dudes.  So, if I were to just use my rifle and shoot dudes, relying on careful aiming for headshots or just killing them, I wouldn't get alot of points, but I would make it through the game.  It rewards you for taking your time and pacing your kills.  Doing that, you get more time to work out environmental kills and use different weapons, getting more points in the process.  Also, there's a strategy to your weapon loadouts.  There are portions, for example, where a sniper rifle is almost required.  They give you a gun then.  You can switch you 2 secondary weapons with any guns you've unlocked at the dropshops, so depending on where you are in the unlocks and how you play, it makes sense to use specific loadouts.  For example, since I played the demo so much, the flail gun and the pistol are my best weapons for skill shots, so I use them alot (racking up skill points along the way, unlocking greater ammo storage for these guns and upgrading the guns i'm not using)
 
Ok so that's all to say there's more to the game than appears at first sight.  One could say the game is a crazy over-the-top shooter that gets pretty repetitive.  On the other hand, what I have observed is that you can certainly play the game this way, but you are rewarded more for 'strategizing' how you play the game.  Not only that, but the skillshot names are cool and seeing you screen fill up with skillshots is rewarding by itself.  That takes me to another point, the UI in this game is really good.  Not too busy, not too minimal, sort-of where I would want it to be.  
 
 
Level Design and Set Peices:
This game is crazy.  The world you get placed in is huge, and it seems like when you're not actively killing dudes, they're trying to show off what they've done with this world they've created.  That's cool and it looks amazing.  There are some amazing in-world events as a result of the story part of the game, and some crazy monsters/bosses you face.  This over-the-top part for me is really really satisfying.  As most of you have seen, the robot dinosaur part is super cool.  It was also challenging as the robot controls were flawed somewhat in the way you would expect them to be (which is the robot dinosaur shoots from it's head, so it's not so much like a big tank.
 
The language/voice acting:
This is what will probably be the most polarizing part.  I like that this game takes itself so un-seriously that the writing feels like it was done by a 13 year old or auto-generated.  The dialog (and story) is absolutely balls-to-the-wall batshit crazy.  And it's better for that.  I think some people look at this like the weakest point, but to do that I'd have to think this game was intended to be serious (a'la Cod, Halo, Gears, etc).  But it's not.  So I'm ok with that.
 
 
Actual Weakness:
The engine.  I like Unreal.  So I like this game, and the style.  It's not too gears-y, which is good because I don't really care for the gears unreal look.  However, Unreal has issues.  Texture pop-in comes up here and there (actually only once in the 5 hours I played and for a cutseen and 5 minutes of game play after that).  What happened was grey's character never loaded right and some of the in-world objects didn't load right either.  The game righted itself very quickly and I got over it.  But nobody likes that, and i hope if that one area is busted they fix it and if it was a random glitch it doesn't happen again.  Part of what I like about the unreal engine is the sizing of everything is more video-gamey and feels a little bit bigger.  People look like they're 7 feet tall, versus the normal height in CoD games and the five feet tall they feel like in Battlefield games.  I think this is a bit of a visual preference that people either will or won't like.  I do, but I can certainly see how it would turn people off.
 
 
Wrap-up:
In any case, this game will most likely be pretty polarizing.  I think the game itself is solid, and reviews and gamers in general will/should see that.  The tone of the game may come under fire (already has) as will the length and extra features.  I think this game is good enough that it coupled with DNF later this year can change the course (which I don't like) of like every AAA shooter to come out for a while now.  However, even if it's not a) I like this game, and b) I think it will end up like Red Dead Revolver.  The forgotten spiritual prequel to a game which later was absolutely amazing, and re-introduced a whole new genre to gamers, the western.  So in either case, this game is refreshingly old-school, and hopefully more new games will be old-school (and good) too.