What I Hope to See in Borderlands 3.
The same Borderlands wit and charm the series is known for.
More loot. MORE LOOT. MORE LEGENDARIES! AAAHHHHH!
Even better shooting mechanics/hit registry/etc. Playing BL1 almost gives me an aneurysm these days because all of the weapons have annoying sway while iron-sighted and even nearly perfect accuracy weapons seem to miss consistently. Or maybe I just suck at shooting in BL1. BL2 and TPS both improved shooting vastly and made guns feel better. I just want more of the same.
Better lore. Hell if we had a codex of some sorts with a few paragraphs, some flavor texts, and interesting pics/drawings of mobs that unlocked sequentially as we murdered more and more mobs (or murdered them in specific ways), that'd be sick. That was one thing I loved about games like Metroid Prime. It just made the whole universe feel more grounded and "real."
No slag-gates for higher difficulties. I couldn't get into UVHM in BL2 because instead of adding more enemy functionality, increasing their abilities, giving them new weapons or skills, upping their tactics and intelligence, or anything else creative that'd have to make the player play differently and with more skill, they just got number buffs and made slagging nearly every enemy a necessity. Just not my cup of tea. :/
The cryo element again. Freezing flying mobs and them dropping to their death was great, and having a way to CC enemies through weaponry was just awesome even if it meant they traded a bit of elemental damage away (if I'm remembering how the elemental damage on cryo weapons worked).
Skill trees inspired by the leaps taken in TPS and with Gaige/Krieg. I loved Zer0 to death and the rest of the BL2 Vault Hunters were amazing, but the skill trees were nearly boring compared to TPS's. If I could play Borderlands 2 with Wilhelm and Nisha you bet your sweet ass I would. Playing keep up with Wolf as he ramped up was some of the most fun I've ever had in Borderlands.
Randomized dungeons with "floors" and the occasional random boss. If I'm going to spend a lot of the game farming and grinding, I'd love to see something unique every time I wanna drop a few hundred or thousand baddies. Even if it's just areas cobbled together randomly with pieces of the map with an assortment of themed enemies thrown in, that'd go a long way towards keeping things interesting. Bonus points if there's a "hardcore" option where the loot is better but you can only leave every 5th floor and if you die beforehand you lose all your loot.
I think that's about it. Feel free to chime in if you want. I was just airing out some thoughts since I'm replaying Borderlands and eagerly await BL3.