Alright so these are my first impressions.
First off, game looks pretty. Gorgeous art style and soaking with atmosphere, love it. However, at times it can feel rather bland, though that might be due to how much we've seen this demo specifically. Design of enemies, characters and just the world really complements the feel that this isn't just Halo, instead it is Bungie's own world. Great job there.
And that is where my enjoyment for this game stops. Everything else is just...not good. The AI is atrocious and stupid, they will literally stand in one position and shoot without really using cover or doing anything flanky. I had a whole bunch of hive just stand there waiting for me to throw my grenade thing and it felt really stupid to watch. I feel like more movement from them and more varying tactics would really help spice it up, but that might be limited with the controller input and reaction.
The audio is great, but dear god what is wrong with Peter. Usually I love his voice but he sounds so dull and bored, it really detracts from the game's atmosphere. Speaking of atmosphere, the game can sometimes feel really empty, which is not a bad thing but I feel like it forces you to mount up for travelling or else enjoy boring walks along empty corridors.
The layout of the map is pretty dull, a lot of places you just can't go to and some will just inexplicably kill you because you decided to explore. Other places have nothing when you do explore, so it feels useless to go walk off the beaten path. Games like WildStar and Guild Wars 2 did this so well in that moving away from the traditional dirt road gave you great benefits, so its annoying to not see this in Destiny.
Warlock. Holy crap it is bad. You start off with an SMG, Assault Rifle and a Shotgun, all of which you'll end up just using the SMG or assault rifle because they have the longer range and better burst. My "abilities" are very limited, and you can only have them assigned as supers which is super boring. I felt like it was pointless having classes because there is no real class structure, everyone just uses guns. The Warlock super is fun, but takes forever to charge up and you can get swamped so hard that it becomes pointless.
UI is alright, albeit clunky. I don't particularly like controllers and so I'd hope to see keyboard/mouse supported as that would ellevate a lot of my problems with the UI and game interaction being clunky.
Of course these are all my opinions however this hasn't really helped push me to buying it, and honestly it just feels like a mediocre Borderlands but without the fun and some Halo themes thrown in. The big problem I have is that while this is alpha and things can change, nothing as drastic as what I pointed out could possibly change in the three months to launch. The game feels like it could be fun for a bit, but I am definitely not getting that vibe of "yeah, I could easily spend hours playing and enjoying this."