In my personal opinion, ME2 was making the right steps when it came to an inventory. I am Commander Shepard, a previous N7 Marine of the Alliance Military, at one-time a Spectre(possibly again, depending on choices), and being backed by a company who's income is in the billions per year.
Why would I think to myself, "Hey, I'll just grab this helmet off the guy I just killed."? Or "hey, another weapon I've already got five of, yep, into the magic backpack - oops, the backpacks full".
Hold on a minute guys, I going to change my armor in the middle of space. Not to mention getting Colossus X armor from a downed probe on Luna or Turian Armor off a Geth Drone.
It makes more sense for a soldier to load up his armor and weapons when leaving the ship for a mission rather then carry it all with him. Picking up new weapons, theres no reason to carry every damn weapon you come across. In the time period, it also makes more sense to scan items and fabricate them myself then to gather them so I can sell to a pawn shop(which most shops aren't - they wouldn't buy your stuff anyways).
I do think they dropped the ball on certain points - there should have been more weapons, weapons should have been customizable, more armor parts, squad customization(not necessarily complete visual control like your player, but at least customized stat bonuses).
Ok, now that that's out of the way, I have a few idea on how to fix it for ME3.
First of all, basics:
*More weapons, with a unique feel and look(ie not the exact same weapon copied a dozen times). I'd say 4-5 of each. Scarecrow's thread had a pretty good idea of a way to do that.
*More armor parts, with better bonuses that make a difference(ie you can feel the difference between someone built for extra shielding and someone built for pure power).
*Moddable weapons, such as modular builds(like armor is), mod slots like ME1s, upgradable trees, ect. Something to make it YOUR weapon. I prefer the first one, myself. Such mods/parts/ect could be researched then equiped on the weapon.
*With the new number of parts for weapons/armors/ect,
Now then, a few points to consider from complaints:
*I've seen some complain about the lack of progessive weapon/armors(ie, using the same weapons/armors throughout the game). We do have it, in the upgrade system, but it isn't obvious. To fix that, I have two ideas: