There seems to be a lot of some-timers going on around 2e. Memories are fuzzy as to what exactly was/wasn't in 2e. Speaking as a purist (IE, never touched 1e...)
Things it took out -- Subclasses. Half-orcs. Monks. Gygax's voice. Clerics became priests. Didn't like initiative rules. Priest spheres were more complicated. Thief skill point fiddliness were more complicated. Demons and devils. Magic item price values. Magic item creation guidelines. Illusionists.
* Subclasses WERE there!!! The difference was they were called "groups" and encompassed classes were certain traits; warriors (Fighter, Ranger, Paladin), wizards (Mage, Specialist/Illusionist), priest (Cleric, Druid, Specialty Priest) and rogues (Thief, Bard). Classes in a group shared the same Spell Progression Tracts (Priest/Wizard), HD, Thac0, Save Chart, WP/NWP rate, and typically the same XP table (notable exception for cleric/druid and fighter and ranger/paladin)
* Half-orcs and monks did disappear and only re-appeared many, many years later. However, how utterly confusing and broken monks were ("you have to have high ability scores, but get no bonus for them") I can say not much was missing.
* While Zeb was no poet, I cannot say I lament Gygax's voice. He wrote a series of long, winding stream-of-conscious essays and called it the DMG, which was a terrible way to learn to DM. It's layout was miserable, it seemed to ramble from one topic to the next without rhyme or reason, and it was near impossible to find any given rule when you needed it. Thank god for one of the best Indexes in all of gamerdom, of the the thing would be impractical! (To be fair the 2e DMG was terrible too, but at least it was well-laid out and searchable terrible).
* Clerics were still in the game. Still called Clerics. Gained access to nearly every spell they had in 1e (and a few extras thanks to the sphere system) and had all the classic cleric trappings (turn undead, blunt weapons, etc). Most DMs replaced them with Priests of Specific Mythoi (Specialty Priests) but generic clerics still were in 2e.
* Initiative? 1d10, lower goes first. Want to add more realism? Add your weapon's speed or spell's casting time. No "always loses initiative" based on weapon size, no segments, no weapon speed to break ties, etc. Simple. Easy.
* How were Spheres of Influence complicated? Your class (be it PoSM, cleric or druid) defined access to a sphere. You either had Major access (all spells) or minor (levels 1-3). Sphere's didn't change once you picked your class. It actually gave divine characters the ability to diversify their spell access without redesigning millions of new classes. (though better rules for balancing them would have been nice).
* Seriously? Thief Skills? You have 60 points at level 1, 30 each additional, and the bonuses for race, class, and armor. It allowed thieves (like wizards with specialties, fighters with specialization or clerics with spheres) to customize and specialize in trapfinding, sneaking, pick-pocketing, etc.
* Yeah, Demons & Devils disappeared until MC8 and then again till Planescape. Baatezu and Tanar'ri didn't bother me though, would devils REALLY call themselves "devils?"
* Magic Item Prices? I thought we didn't like Magic Item Shoppes?
* Ditto with creating any magic item in the DMG.

I liked that magic was soley in the hands of the DM, and that he decided cost and ritual needed to make magic. Granted, I also like Magic Shoppes too...
Bards cast more damaging fireballs and lightning bolts than magic-users of equal experience points. This gets really distorted in high-level play (which our group did a lot of). When a bard achieves 20d6 fireballs, a magic-user is casting 15d6 fireballs.
- I think that priests of specific mythoi are too open-ended for the player's handbook. I'd prefer them in the DMG along with plenty of well-balanced examples. I'd like to see only the basic cleric and druid in the player's handbook.
Bards and wizards (mages and specialists) cast at the same caster level = character level. The difference was bards started as 2nd level casters (since they didn't cast spells at 1st level) and progressed slower to new spells levels, capping at 6th. However, a 15th level bard and a 15th level mage cast fireball at 10d6 (the cap).
The Cleric was the default "priest" class. Druid was given as an example of a PoSM, along with some suggestions on how DMs could make additional PoSM. The problem was the rules were too vague to be any good, resulting in PoSM ranging from crippling weak (Complete Priests Handbook) to Godlike Strong (Faiths & Avatars). (My personal favorite was the crusader/monk/mystic/shaman classes in F&A/Spells & Magic. Balanced against the Cleric/Druid, flavorful but generic enough to work. If I ever ran 2e again, I'd use Clr/Drd/Crs/Mys/Mnk/Sha as my specialty priests and ignore PoSM).