Fate Core, even as a draft, contains some of the best GMing advice I've ever read. It's a fundamental revelation, like the first time reading a system that didn't use levels, or classes, or random die rolls for attributes, or random damage from weapons. Even someone who runs a non-Fate game can benefit from this stuff.
The recurring theme throughout is something I've subconsciously understood when running games, but never gave a lot of thought about: how does this add to the game? We are told in various ways, in various sections, to make things matter. If you can't come up with a compelling reason for a die roll, or a ruling, or a story element, then you need to rethink it a little bit. If it doesn't do something to move the story forward or challenge the PCs, maybe it doesn't need to be there. Chapter 9 - "Scenes, Sessions and Scenarios" - is a particular goldmine of wisdom on examining various elements ranging from the relationships between the PCs, other characters, the world, and various other connections for getting a scenario going. A GM doesn't need to have Aspects in their game to take advantage of the methods Fate Core suggests.
In "What Makes a Good Fate Game?", three basics are laid out: competence, proactivity and drama. The characters are competent at what they do. Situations shouldn't exist unless they let the PCs show off their competence. When things go pear shaped, it's not because they didn't know what they were doing, it's in spite of their competence. Maybe the plan doesn't go right, or there's something beyond their control. The PCs are also proactive. They get involved, they do stuff, and don't just sit around waiting for the adventure to come to them. Finally, there need to be complications and difficult choices that the PCs have to make. Nothing should be single-faceted, unless that in itself is interesting and moves the story forward.
I've played in games where the GM seemed to only focus on setting our characters up for failure. They weren't fun games. Nobody wants to be forced to make a Dexterity roll for no reason other than to open a door - not an important door, not because the character is being chased by a demon, but just because the GM randomly decides it's a thing to do. Similarly, I've played in games where none of the players actually had their characters do anything. The PCs sat around like lumps, waiting for the next plot point to find them. The only way to get them engaged was to set up a fight, and even those turned out mechanical and boring because the players weren't engaged. They didn't have any skin in the game besides the scribbles on their character sheets. Fate Core's advice does a lot to counter these types of things and I can see how employing some of the techniques could help pretty much any game.
Obviously, some GMing styles might not mesh well with this. If you're someone who doesn't really like metagaming - or are a "let the dice fall where they may" type person where chance encounters are expected to be deadly - competence, proactivity and drama may not be the best fit. Even so, the higher level idea of make it matter should still be a takeaway. If a character is going to get an infection from a random injury they sustained, it should matter somehow. If you're going to call for a die roll, at least think about how that die roll might turn out. What happens if the character fails? How can it lead to additional complications? What are the stakes? Those are questions I'm going to be asking from now on, regardless of what game I'm playing.