I want to go the Black City. I want to walk in there and finally find out what that place really is
I want to see it, but not before DA6: first have the writers tie up all the loose plot threads left hanging (the Qunari/Tevinter conflict, whatever's brewing in the Anderfells, Solas misbehaving...) and keep the Black City for the grand finale.
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Pet (not as a companion but rather similar to the mabari in DA2)
Nah, if they reintroduce a Mabari, I want them to go all the way: give the pooch a customizable skill tree filled as it levels up, make it female, and give her her own romance sidequest ending with a litter of puppies 
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If we go to Tevinter then I want a more in depth look at the politics that are currently going on. The party of Maeveris vs others. I feel like they really wasted that with the civil war in Inquisition.
Ha yes, more cloak and dagger politicking. But that shouldn't be keept in Tevinter only: Inquisition implied that both Qunari society and elites weren't ideologically homogenous: depicting the inner dissension among the Qunari would be a great way to portray them as something more interesting than horned Borgs.
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Besides, they need some reason why your character needs to hear exposition, because they need some excuse to give exposition for the sake of players who are just arriving at the series and don't have any idea what Tevinter is.
You could have the PC doing the exposition for the player's sake: let' imagine an hypothetical conversation between the PC and Dorian about one hypothetical minor antagonist:
Dorian: Lord Truchmuchi is a young, ambitious member of the Publicanium
Foreign PC: What's the Publicanium?
Tevinter PC: The senate's lower house is virtually powerless, how could this glorified bureaucrat be a threat to us?
One answers gives Dorian the opportunity to do his exposition about Tevinter's inner political workings, the other one acts as exposition for the player's sake.
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DA:O actually went against the lore by allowing us to spec as a healer
I'll give a pass to Origins about that: Wynne was an experience healer with decades of experience, the Mage Warden was a freak of nature and the poster child for how broken the circle system was (here's a mage who's pretty much capable of going on a genocidal rampage on a whim, let's allow him/her to roam the land freely, then rule a whole Arling thanks to a convenient legal loophole while the Templars keep themselves busy bullying the much weaker circle mages) and Morrigan's the daughter of an Elven goddess.
Personally, I wouldn't mind the healer spec to work like DA2's: the amount of skill points needed and the cost of healing spells were high enough that you had to sacrifice Hawke's offensive abilities in order to to turn him/her into a competent healer: Healing was very useful, but came at a steep price.
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I watched some footage of the new zelda game. There were many things that da4 should/could implement
Mute protagonist! Opening section devoid of NPCs! Giant boar as the final boss!
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8-introduce swimming-drowning in a puddle is just wrong
I don't like watching characters in heavy armor swimming. If anything, I'd like swimming being linked to the armors equipped: if at least one character wear middle or heavy armor, then the PC won't accept going farther than calf-deep into the water. If everyone is wearing light armor/clothe, then swimming is allowed.