Pretty please keep the world map system. It is beautiful, and open world is not happy times for story intensive RPGs. That said, I think some larger, less linear parts of the game would be nice. For all its appearance of non-linearity, DA:O is actually an extremely linear game, with pre-set tunnels you travel down. I think that a larger, non-linear hub would be excellent. This would be a city, like Denerim, just with more than one meaningful area to explore. This leads to...
Better side quests. Not to complain, but it seemed like almost all of the side quests were just those silly job posting things, or hacking your way through a brief area. I'm thinking of stuff along the lines of the ones Slim Couldry gives you. Or, you know, ones where you have to do more than just collect items. DA is hedging closer to a MMORPG, where I honestly think the game would be better served by being less of that. Yes, I know that they are all the rage with the kids these days, but there's a reason the sidequests in WoW are so shallow: they have to be. Single player allows for a lot more. Take advantage of it.
A real, compelling villain. Come on Bioware, you're the only game company ever to do it right with Irenicus. I know you can do it again. Someone who foils the party at every turn. Someone with complex motivations. Someone who is so much fun to hate.
This may be unpopular, but an entirely new character, starting from scratch in an entirely different setting.
Keep origin stories. They weren't all earth shaking, but the concept is fantastic. On that topic, more classes. The current ones are a bit limiting in what you can do.
Better thought out skills. There are too many useless, throw-away skills, particularly at high levels (::coughfeigndeathcough:

. And more spells! More spells is always fun. Perhaps force mages to specialize a bit more in what spells they take so it is a little harder to create the one obvious best mage.
More unique specialization, i.e. more things that are like Arcane Warrior. Things that actually change your character and play style rather than simply making you more zomgSMASH.
No giant epic battles, wars, etc. It works great in movies and strategy games, not so great in RPGs. The endgame was by far the weakest part of Origins. It is perfectly possible to have a grand story line and thrilling battles without any armies involved.
I don't care about a bigger active party size, but just keep up the same standards for the companions that you've already set, and strive to improve. The romances, friendships, and rivalries that can develop intra-party are the highlight of Bioware games for me.
From a more technical/game design standpoint, get rid of the inventory limit, or at least make it more apparent how much stuff there is. Contrary to what some designers seem to believe, inventory management is never fun. It is not an interesting choice, it is just an irritant. Additionally, allow access to the world map from any non dungeon area. I'm mostly thinking of the Brecilian Forest here, but it is really irritating to have to walk back through large empty areas just to reach the map.
And finally, don't rush like with Awakening. It's painfully obvious that it wasn't finished, unlike Origins. Wow, that was pretty long-winded.