I've just played about 5 hours as well, got Zer0 up to level 12 solo and Axton up to level 8 in co-op. I've found some pretty nice weapons, including: A sniper rifle with a massive sword bayonet, a sniper rifle with a pair of rotating barrels that does a 3-round burst when scoped,
this which I think will be my go-to sidearm for a while and an assault rifle with a 6-round magazine which basically fires rockets, which was a bit odd. No actual rocket launchers yet, though. I've also found a few class mods for Zer0, including a health regen one.
The game has a couple of weird technical issues as far as I can see. One is that there's a strip of pixels at the bottom of the screen which are all random colours (you can see it in the screenshot I linked, actually) and sometimes I get what can only be described as a red glow at the bottom which is clearly not supposed to be there, I've got a screenshot of that on Steam too. If you press F in the inventory to get the image of an item plus stats as I linked above then press P to take a screenshot of that, I get a random corrupted image but my friend I co-oped with said it worked fine. Also the quest 'Bad Hair Day' seems to be bugged, has anyone else tried to hand it in to Sir Hammerlock? I gave up in the end.
For now, though, I think I should sleep... I really want to carry on but enough is enough!