It's been ages since I played AD&D 1E, so these memories may be a little confused. As I recall, there was no unified skill system. You had such and such percent chance to be able to climb a rope or jump a certain distance, but they were all just table after table of lookup. Every class had its own table for all manner of common things. When I played AD&D, my friends and I had memorized all kinds of tables, or at least the page on which to look. (I seem to recall that an important lookup table is on p. 91 of the 2E PHB.)
Second edition simplified a lot of things by creating proficiencies and the THAC0 system and a few other simplifications. Third edition streamlined things even more, reducing almost everything to a d20 roll. I had sort of expected 4E to go the distance and give us something like the True20 system, in which you only need a d20. Instead, it's just another few steps along the path that we were taking. There are fewer distinct game concepts representing the same things, which means that the game is easier to learn and adjudicate. I'm definitely in favor of that.
The big simplification is the creation of "powers." The powers system (which strikes me as totally ripped off (in a good way) from Mutants & Masterminds) is used to define, well, powers. Any random effect that your character can cause to occur is a power. In 3E, this was represented in part by feats. Feats could be used to perform special attacks, and for this reason fighters got lots of feats. In 4E, feats are still here, but they're much less important. For the most part, they're something like "merits" from the World of Darkness games. They give you bonuses to stuff under some circumstances or because of certain properties of your character. They don't ever grant you new abilities, unless they do so by granting you a Power.
Powers can be used either "at will" or "once per encounter" or "once per day." They all have a power source, a range, an effect, and so on. If you understand how powers work, in general, you will do pretty well at understanding any special ability that any creature possesses at any time. Spells are no longer their own thing with their own rules. They're powers. Special fighter attacks are powers. A cleric's prayers are powers.
Beyond simplifying things for adjudication, this has some significant effects on how the game will play out. For example, Magic Missile (a spell used to attack the darkness) is now an at-will ability, meaning that if you are a wizard who knows this spell (read: has this power) you can cast Magic Missile every turn until combat is over. Your wizard will never run out of spells and have to throw darts or hide behind the half-orc -- I mean behind the dracosaurusman. This doesn't eliminate spellbooks: your wizard still has one, and it has more spells in it than he can use in a day. So, for example, if your wizard can have a single once-per-day power, your spell book may include two. You pick which one you are going to have prepared, each day.
This means that you can run out of some spells, and you still have the ability (and dire need) to plan your daily spell inventory carefully. I think it's quite an elegant solution, because it also seems to work well for fighter powers (special attacks) and magic items and monsters.
This also means that there's no reason for fighters to get more feats (or powers) per level than wizards. A power is a power. In fact, all characters progress the same way as they gain XP. Level 5 characters will all have the same number of feats, powers, skills, and so on -- or they'll at least have gained the same number by virtue of simple class progression.
Of course, this wouldn't work very well in 3E, because of the distinction between class level and character level. In 3E, you could be a second level fighter and sixth level bard, meaning you're an eighth level character. In 4E, multiclassing is greatly stripped down. You are always a character of one class. You may "dabble" in one and only one other class, meaning you are able to chose from some of its features as you progress. If you're used to 3E, It might take a little while to get your head around 4E multiclassing, but it's extremely easy to understand once you do. It's certainly much simpler than the first two editions. (Hey, who remembers dual-classing your human?)
There's a really nice little gem built into character progression. Each level, you're allowed to say, "When I decided I wanted to know 'Summon Monkey,' I was on drugs. It's not useful at all. I would like to retrain myself to forget that and learn 'Summon Lemur.' That seems much better." This means that you can be a little less anxious about making sure you pick the "right" skills over time.
There are some other changes toward that end. Skills have been extremely simplified. Rather than rating skills from 1 to 20 (or 1 to Inf, I suppose) you either have a skill or you don't. Some skills are only available to some classes. I'm undecided about this change, so far. On one hand, I'm glad I'll never watch a player waffle over putting that one extra point into Bluff versus Diplomacy. On the other hand, eventually the bonus from having a skill becomes less significant.
A basic skill check is something like:
d20 + ability modifier + ( .5 * character_level ) + (5 if trained)
For a 24th level fighter with a high dexterity, this might mean a base skill check bonus of 15 for an untrained Thievery check. Sure, the extra +5 would be nice, but why on earth can some brute do so well at picking a lock? The description of the Thievery skill says that "the DM may decide that this skill may not even be attempted if not trained," but that strikes me as a cop out. Either there are "trained only" skills, as in 3E, or there aren't. Don't just sort of hint that it might be a good house rule!
Speaking of things you can learn, once again languages suck. That's okay. It's not usually a big deal, and I've never seen an RPG in which language learning seemed in any way realistic. What bugs me in 4E, though, is that there is no way to "learn to speak Elven." Learning a new language requires picking up a feat that allows you to read, speak, understand, and write three new languages. The problem, of course, is that a feat for one language would be a lousy buy, given what other feats can do. A language isn't a power to acquire, and you can't gain more pips in skills easily to make it a function of skill acquisition. Oh well. I think that as usual, PCs will learn new languages by begging the DM for them.
I only skimmed most of chapter nine, which covered combat. It had all the usual rules for things that I never bother with. I'd love to be able to easily learn and remember all the rules for flanking, cover, grappling, and so on. It would be great to take advantage of all the playtesting that has been done to help combat work well. It's just too much stuff!
I'll probably read the chapter again, more closely, but so far it looked a lot like previous editions. It did use top-down pictures of grids with miniatures to good effect, though, for explaining things like flanking.
Tomorrow, I may start to read the new DMG in earnest. Maybe in a week or so I'll have some thoughts on that.