I guess I've been lucky, in that since my friend hasn't had time to play recently, my experiences have been all solo, and generally decent. I've got decent loot as I've gone. Sure, I've kept a gun for a number of levels, but that's not because I haven't got a better one, it's because I tend to get attached to a specific style of playing, so if I find a better gun that works slightly differently, I don't necessarily switch.
But I've found lots of purples, plenty of oranges in both my main playthroughs. I've had a bit of "loot disappearing underground" going on, but I don't think anything too serious.
My main annoyances:
Game balance - especially boss fights - seems aimed at multiplayer. Some of them are freaking insanely difficult if you don't terrain exploit. I'm sure they are much easier when you've got someone that can pull you back up if you drop, but if you don't, you're screwed. Same with some of the pure fight challenges (the "survive X waves" ones). You can go 20 minutes through a round, hit a bad streak of luck, and go down with no one that you can kill to get back up. And so you have to repeat the whole damn thing. Very tedious.
Not enough storage. Ugh. Games never seem to give options for packrats. I tend to hold on to things. I never want to sell a purple or better, for example, even if I'm not going to use it. I might want to give it to another character! (probably not going to happen, but I like to hold on to things anyway) And yes, you can upgrade your bank and personal storage, but only to a point. I can easily fill that space, and have little left. Which is annoying when you like to pick up everything. I've got plenty of Eridium to spend, but nothing I want to spend it on. It's even worse on your second run through - I was expecting to be able to buy more upgrades. Nope.
Better weapon descriptions. It's really weird, sometimes you'll have a gun that says "uses 3 ammo", and it does, sometimes you'll have a gun use 3 ammo when it doesn't say it does. Or sometimes it'll use 3 ammo only part of the time. For example, I was using a Dahl? gun - whichever does the burst-fire when zoomed. When unzoomed, 1 trigger pull uses 1 ammo. When in zoom mode, it does burst-fire, which of course is 3 shots. So it should use 3 ammo, right? Nope, uses 9 ammo. Apparently each burst shot is using 3 ammo for some reason. And of course there's nothing that tells you it does that, I just noticed I tended to run out of ammo faster than I was expecting.
Similar to the above, I'd really like number integration. You get Badass levels that gives you +X% faster, say, reloading. Then you've got a skill that gives you +Y% faster reloading. Then you've got an artifact that gives you +Z% faster reloading. So how fucking fast do I reload a gun? I mean, yes, I know it depends on the gun itself, but why not have the tooltip box actually list the functional reload speed, not just the gun itself?
That's about all the ones that jump into my mind at the moment. I'll probably think of some others later. I should point out that despite the annoyances, I do think the game is pretty damn good.