How would you improve classes in DA4?

First and foremost, I would bring back stat customization. Any class would be able to use any armor and weapon combination, provided they have enough Strength/Stamina/Dexterity. It might mean your Mage would suck at spellcasting, but that's the trade off.

For Specializations, I would create a hybrid system between Origins and Dragon Age 2 where characters have one specific to their character, and an open one assigned by the Player. I actually liked DA2's unique specs, as it made sense in the lore and gave players incentive to use all of the characters. However, I do agree that they were too rigid in function, and it made zero sense that Merrill didn't know any healing spells as a Dalish First, among other things . So bringing back multiple Specializations would alleviate some of that.

I would bring back healing spells for mages. Spells that are very similar to one branch of the creation tree in DAO.

I'd also bring back the Spirit Healer specialization. And for warriors I'd absolutely bring back the berserker spec.

Warrior: Go back to allowing them to use any weapon again, with skill trees devoted to each. Make them masters of weapon damage and (potentially)damage mitigation.

Rogues: Give them crowd control abilities. They can do modest damage normally, but let them emphasize on being able to maneuver through combat unhindered (stealthed) while debuffing and crowd controlling the enemy (stuns, damage over time, slows, damage debuffs, etc). Give them a few devastating attacks that require some setup to achieve.

Mages: Their strength should be versatility. Go back to the four schools of magic and let players decide what kind of mage they can be. Glass cannon? Healer? Crowd control? Summoner? They shouldn't be able to do everything, but should have access to a wide range of possibilities. Not just "blast with fire" "Blast with ice" or "blast with lightning"

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A lot of this was discussed in the "merge rogue and warrior" class thread, but, fwiw: don't have classes. That's the best thing to do with them. Any build can pull from any skill tree.

Rogue split into
Rogue (melee: daggers, subterfuge) -> can specialize into an assassin, illusionist/shadowwalker (enhances the stealth experience) and scout.
Scout (ranged: bow/crowssbow, sabotage) -> can specialize into an alchemist (tempest), a trapper (artificer) and a thief

Warrior splint into
Barbarian (twohanders, dual wield onehander, battlemaster) -> can specialize into a reaver, a weaponmaster (dual wield twohanders, anyone?) and a fighter.
Fighter (onehanders, shield, vanguard) -> can specialize into a champion, templar and a barbarian.

Mage split into
Elementalist (glass-cannon high dps mage) -> fire master, lightning master, ice master
Necromancer (summoning, curses, debuffing) -> undead master, blood mage, entropy mage
Druid (crowd control-happy, a jack of all trade, master of none mage) -> shapeshifter, force/rift mage, ???
Cleric (onehander + shield, tanky healing, buffing, spirit magic melee combat mage) -> knight-enchanter, spirit healer, ???

This will never happen, of course, and are probably somehow lore-defying. I just want more elements into building a character, really.
Rouge, warrior and mage just isn't enough for an RPG, it really isn't. 

The problem is that both keeper and creation are both very much already included inside the druid and cleric tree, in my mind at least.

But I'm thinking that a further proficiency in nature magic could be a good specialization for druid, like causing natural disasters: earthquakes, volcano eruptions, tsunami, drought. 
Something relating to space and sun could be cool to.

For cleric, I guess a more straight forward spirit mage specialization that is a more reminiscent of an actual mage class.

3 different types of mage class - elemental, battle mage, creation mage
Elemental can control all elements and weather, fire, floods, storms, sun, electricity damage etc.
Battlemage can use weapons other than staff and depending on the weapon can have different magical abilities.
Creation mage is more healing and buffing magic etc.

I like the rogues and warriors in DAI so that you can use two weapon types.

I'd also like auto heal after combat again. But we probably won't get that.

Like I said, all that was hashed out in the other thread: bsn.boards.net/post/90071/thread

TL;DR, yes, it requires an exception for non-mages using spells, but the lore is already full of exceptions, for example, Valta at the end of Descent.

Return to something nearer the choices we had in DAO for all classes.

It makes no sense that a warrior cannot use a bow. In DAO they were limited as to which type of bow they could use by their dexterity. That made sense. They should also be able to play any style, sword and shield, two handed or dual weapon but again their expertise is governed by how much they have trained in it. Bring back Spirit Warrior as a specialisation. It is clear that this is what the Seekers use, not the Templars spec. In any case the Templar spec will not be appropriate if we are in Tevinter since they do not have Templars (just Imperial soldiers serving the Chantry who they call Templars but aren't). If it is possible for a warrior to form a bond with a spirit, you can bet the Imperium would be aware of that fact and have at least some organisation somewhere that teaches it. Wouldn't mind if they introduced some new specialisation as well.

Rogues should be able to be both an archer and a dual wielder and be able to switch between weapons mid-battle (same for Warriors). It just makes you that bit more vulnerable to attack while you are doing so. The limit on which weapons they can use should be governed by strength (for swords, axes, etc) or dexterity (for knives and bows) just as it was in DAO. Bring back the Shadow specialisation.

For mages bring back the spell schools, from DAO in particular but if not then at least as many as DA2. Bring back Arcane Warrior but perhaps as a hybrid of how it was presented in DAO and DAI multiplayer, so can use armour and weapons but also have some Fade abilities that make it seem like an ancient elven art. Bring back Spirit Healer, and Battle Mage and Keeper from DAA, although I admit that Keeper might not make sense in the context of Tevinter.

Give companions their own unique specialisations. That way they can be tailored to suit their origins and background story, plus you have a reason to use them and you won't be taking a specialisation that duplicates their abilities. It made no sense for Cassandra to have Templars spec(she should have been a hybrid spirit warrior), it seemed something of a stretch to discover the Knight Enchanters serve the Divine when we had never been told about them before (and in any case why would Vivienne have trained in that since she never served the Divine?) and to be honest I really didn't see why Dorian was a Necromancer, when that was never anything to do with Alexius' field of study and he had trained under him. (I know he recounted some interest in the Nevarran magic as a child but I really didn't buy that explanation).

Some solid ideas in here
Quite a few of them echo things I say often - not sure what this 'DA4' is though