I like what they did with Barbarians, they can fight topless again. I liked the Monk's unarmed fighting improvement including flurry.
I really love the Bard. Did anyone else notice that Bard magic is not arcane, its specifically unspecified and possible uses multiple power sources. They couch the fluff in terms of Bard spells as just more scraps of knoweldge he or she picks up here and there. College of Valour is perfect for those that wish to play an Gish if one decides that spells they've aquired are arcane. Getting 5 spells from any classes spell lists can lead to some funny stuff, like a Bard that picks Hunter's Quarry from the Ranger, Disintigrating Smite from the Paladin, the Paladin's Oath Mount spell when it comes out, Find Familiar from the Wizard, and Wrathful Smite from the Paladin.
Paladin. I find that Paladin's can choose Archery fighting style kind of funny given they don't have any ranged weapon profiencies. They can take the Archery Mastery Feat or use thrown weapons, but honestly very much a suboptimal choice.
Paladin's mount will be a spell, as others have mentioned. This means the Bard can ultimately steal it. Still its gives mounts flexiblity. My bet is the spell will be very simular in design to find familiar, but more powerful. So you get a list of possible mounts, you summon one permantly and can summon or dismiss it with a minor ritual. Just a guess.
When I first looked at the Paladin I did not like it, as it lost alot of Oath features including thier mount! Should have read the read this document first! Spells are way more important for this verison of the Paladin. The most awesome thing is the new Paladin spells like smites, cruasader's mantle, and Elemental Weapon, and auras. The smite class feature is more useful to multiclass Paladin's then to full Paladin's as the Paladin gets really cool smite spells. Looking at the multiclass tables a 10 Paladin/10 Mage can cast up to level 8 spells which means this character can do a 9d8 radiant smite damage by spending a 8th level spell slot something a full Paladin can't do (although 20 level Paladin with Disintergrating Smite is likely to be a more powerful Smite at 5d10 plus improved Smite's 1d8 if the target fails its save for an additional 2d10 each time it fails).
Personally I'd make aura of resolves, divine health, and aura of courage Oath features of devotion again. Sacred Weapon means if one starts at level 3 strength and Dex can be treated as dump stats and the Paladin can still be an effective melee fighter if she has high Charisma.
Paladin is also the most resource fiddly class as one has to keep track of Spell useage, Lay on Hands points, Channel Divinity, and Cleansing Touch, which I actually like. A Paladin who chooses Protection as thier fighting style is your bff, his aura protects you from fear and charm and Aura of Protection adds his Charisma to your saving throws, and he can use his reaction to grant disadvantage to attacks against you, can heal you via Lay on Hands or buff you via spells.
Paladin's are also the beings that Succubi wake up screaming terror of. She can see through your shape shifting, is immune to your charms, and can share that immunity, her smite can send the succubus back to the lower planes, and She can even turn the Succubus and any other fiends she summons like undead, even use it to kill her. Seriously if I'm a Succubus I just flying away if I ever see a Paladin of the devotion Oath coming my way.
Cleric feels very 4e with Channel Divinity 3 times before short rests, daily spells including healing word, and even at will Cantrips (Orisons), and War Priest Domains. Settings will grant deities instead of domain giving a more 2e speciality priest feel option.
Rangers, I still don't like favoured enemies, I'd rather favoured terrain as subclasses.
Mage needs to explain how one trades out wizardary for other forms of magic. Removing the evocations resistance ignoring is disappointing.
Multiclassing one should just use which ever casting stat one chooses from the classes one is a member of.
Fighter I really miss the Knight.
The one thing that really bugs me, insanely is where the heck is the Warden and subclasses like that that we were told would be in the packet? Hopefully they will be in the update.