Personally I am less concerned about trading in Diablo 3 than I am about the economy itself. Gold has to be worth something. I know D2's item-based economy was not intended, but creating that giant rift between the have and the have-nots is horrible for the economy. In terms of the actual trading, I've always been partial to the Auction House style system, in World of Warcraft, as well as other games with a similar system. It need not be an actual auction house though. There could be "trade" servers where people can come to trade and set up booths of some design where they can offer up their wares for others to see, although this encourages AFKing while you wait, and that is likely not something Blizzard wants to do. Basically I would personally like to see a system where I don't need to sit in the chat all day trying to hawk my wares, I can be playing all the time and let the system do the work for me. Similarly, if I am looking to buy something, I don't have to try and hunt someone down for a trade or purchase. Of course I don't think that these things are elements that should be completely removed because some people enjoy that type of thing, but I would at least like the option. The most likely option would likely be some sort of auction house like interface in the battlenet channel itself.This one is a bit of a long shot, but it would be cool if we had some sort of account-wide storage option, to remove the need for mule characters.
Other than that the only big thing that I would like to see change in D3 is the ability to respec. I know this has been a topic of fierce discussion in the past and present, though I have read almost none of it so I do not know what arguments have been presented for either side, or where the discussion is headed. I simply prefer to have one character that I can experiment with rather than being forced to make 20 different ones to do so. I am the type who loves to experiment, but being forced to create and level an entirely fresh character kills my will to do so. I don't end up experimenting, and I end up sticking with the character I have leveled, worked hard on, and grown attached to regardless of how good or bad their build may end up be