Had my first foray into popping into online this weekend (with this and any game) and the experiences were pretty positive. I'll save you the boredom.
Joined some lv 50 Games, got the Terramorphous achievement, and played a bit of the first two DLCs even though those were normal mode. But there were exploits abound. A couple of people looked like they were standing there Evil Smashering. The first Terra kill I saw he went down in one second.. his health bar didn't even show up. Duels were pretty much 'who can one-shot the other player first'. One person (not the host 'cause I saw them join) in Hammerlock wandered off and took on Voracidous alone. And there was what I assumed was pointless showing off by relentlessly shooting at the Target Practice.. I mean I did start by building a bit of my Anarchy, but then the other guys, none of them Mechros, starting doing it, too.
Also this kid kept bugging me to dupe my Hydra for him. He was the host and I was scared he'd kick me, and I couldn't get an answer as to whether he even had the Hammerlock DLC.
But I was really impressed with a few sessions with people in the lv 20s. Sure there wasn't any scouring of map for vault symbols or area challenges, but everyone was cooperative. There was no ninja looting whether of drops or chests. Fighting for the most part was strategic, group staying together. I chose to respec'd as a support Siren, provided slag, and was even assigned designated driver. So sometimes while they were completing simple objectives, I hustled off to get a vehicle and parked close to the others.
Don't mean to sound lame but I was kind of awed that people waited. Whether in the vehicle (if I wasn't driving), or elevators, or before fast travelling. There wasn't a chat party so I guess people could have been impatient, but no one was moving around restlessly by elevators, going back to fetch a straggler, or trying to fast travel over and over while someone was still in a menu. I was the straggler at one point at a vending machine, and when I turned and saw they were all in the car, I went "oops - oh wow, they waited". Driver wasn't honking.
tl;dr: I had the impression from these boards that you take your chances with randoms, so don't come crying to us if, like, those chances were taken, by you. I guess when games are level 50, people have already done everything and are more focused on gear, and maybe in lower levelled games they ultimately just want to bring characters to 50. But in the lower ones I liked seeing players being a co-operative team and completing missions together. And not being such greedy guts.
It's raining luggage and babies and limbs and Daddy doesn't come home.
It's a very mixed bag, and very high into the evil smashing unfortunately, even just to take out regular enemies. :/
But I do still enjoy it from time to time with randoms, just have to be the host like suggested above and use the kick feature to the fullest. If you see random smasher explosions, kick. If you see someone constantly just grabbing everything in sight without even looking, kick. If you see anyone trying to travel nonstop while you're clearly trying to finish up a sidequest in that area, kick.
Though if you choose to just be more carefree and join, just have to leave. Since it's not your save, no real investment. Sucks that there are so many reasons to want to leave for me, but it's a necessary adjustment in order to have the convenience and flexibility that is public lobbies. :(