My first exposure to Fate was in 3rd edition, with Spirit of the Century, which introduced it. I spent a fair amount of time trying to understand the rules, but whenever I thought that I had it, I would stumble across a rule that I'd forgotten.
The Fate Core System book has, so far, remedied many of SotC's issues in two main ways. Firstly, as a separate core system book - with settings available in supplements - the book itself can be organized into chapters that are actually about the rules. This should make it much simpler to get refreshers on how things work, and it should also make it much more common to re-see things, even if I wasn't looking for them, because they're in appropriate sections. Also a plus: Whoever did layout does seem to have done his best to make sure that each section is in whole-page increments - 1 page or 2 facing pages when possible.
The second, and probably larger, way in which things have been improved relates to Fate Core itself. For starters, reducing the default aspects to 5 per PC should make it easier for players and GMs alike: Even in Spirit of the Century, it seemed like 2 childhood aspects and 2 Great War aspects was excessive, and the list could have easily been trimmed to a more manageable 8. I also don't have to remember that the limit on the bidding war for a Compel is 3: Now, the PC can just buy off the compel at 1, done-and-done. Reducing the number of Stunts to 3 should also make things easier to track, and I'm fairly certain that starting the Refresh Rate to 3 will get the Fate Points flowing much better than they might have before.
I also heartily approve of breaking skill uses down into 4 types (not all of which apply to every skill - specifically, most can't be used to Attack), and the various
I haven't finished the read yet, but I have the feeling that, when I'm done, I won't have much left to double-check. All in all, I'd say that this is a good system.