1. Absolutely, Positively No Over-Clever Aspects. No. None. Zero.
Aspects should be straightforward as possible and concrete as possible. This doesn't mean they have to be physical within the game world. They can represent emotions or points of view of the character or faction that has the Aspect. In fact it's good to have Aspects like that (see below.) But everyone that hears an Aspect should have (or be able to get with a simple question) a clear picture of how they exist inside the game world and in what situations they apply or don't apply.1A. Anyone bringing an Aspect to the table based on a pun, or trying to use them in a way that is based on a pun, must receive a 7+ minute long lecture on what Aspects are.
1B. When you use Aspects in any action you should be able to, in a sentence, say what the action is, and use the Aspect in that sentence, in a comprehensible (if not grammatical) way. If you can't understand what you're saying then the Aspect doesn't apply. "I'm a Trained Physicist, so I'm used to dealing with industrial computer systems on the fritz; my training will help me hack this one." is comprehensible. "I'm Brave, and I'm in a dangerous situation, so being Brave helps me beat up the bad guy in this dangerous situation" makes no sense. Being Brave might help you Overcome some kind of despair, provocation to fear, or Defend yourself when the other guy is trying to Create an Advantage for themselves about how scary the situation is. But it isn't just a generalized "I'm in danger? So Bravery helps me." thing. That's not what Bravery means!
1C. The GM should be an absolute dick about refusing to permit Aspects that only obliquely apply to be used in an action. Remember that Fate Core is an action adventure system, just as much as D&D. Aspects only apply or don't apply to concrete actions occurring in the world. (The exception is if you're invoking one to create a detail; this works perfectly as-is and nobody gets mad enough about it to read a blog post, so just ignore that exception for now.)
1D. Just about every session the players should be changing at least one character Aspect to respond to the situation that they urgently find themselves. This is an anticipated part of the game (carefully read the minor Milestone description) and should be made almost mandatory. This is another reason over-clever Aspects are bad. You won't want to give up an Aspect you worked really hard on, but you'll easily give up an Aspect that is simple. See 1 and 1B.
1E. The one exception to this principle is maybe the High Concept, where something really baroque and weird can be appropriate. That's where you say "this is my thing", so go hog wild with it if you really feel the need to go hog wild somewhere. The GM should still be aggressive about not letting it in if it doesn't apply though - that's how you get fish-out-of-water comedy friction!
2. The Acting Entity Generates Their Total and the Reacting Entity Tries To Beat It. Absolutely, Positively No Exceptions.
2a. The number one complaint people have about Fate is when you're just sitting there piling up Aspects on both sides. "Well if you do X then I do Y and invoke aspect Z." No fuckin way. Don't do this. For one thing, see 1C above. For another thing, an action in Fate is a declarative statement, and you don't get to just rewrite it as you go. You make the statement and the other side makes a statement in return.
2b. Note that by doing this, Create an Advantage is valued more by actors than by re-actors, but fate points are valued more (and spent more) by re-actors.
3. Fate Accelerated is a Great Idea but the Default Approaches are Bad.
3a. The default Approaches reward over-cleverness with language. I absolutely promise you some shithead lawyer is going to be able to explain why they're attacking you Peacefully. Who the fuck wants to even hear that, let alone have to "adjudicate" it. No way. If you must use the default approaches, be prepared to be just as much a jerk about which Approaches apply and which ones don't.
3b. Dresden Accelerated is a little better on this because the supernatural stuff sorts really firmly into the approaches. But you can do even better than Dresden by remembering that the Approaches should be as concrete and well-defined as possible. It's really important to know where the boundaries of broadly defined stuff is.
3c. Don't overlook Fate Core just because you're excited at how simple Fate Accelerated is. If you find you're drifting off into space when arguing with yourself about NPC stats or whatever, just go back to Fate Core!
4. Almost Always Try To Tie Your Power System To The 4 Actions.
There's lots of different power systems in Fate. Their worst failures are when they don't actually help the players get through the 4 core actions of Fate. (This is also why the best stunts are those that alter or expand on those 4 core actions.)
4a. If you're thinking about how to adjudicate the use of a power in Fate, think about the 4 actions. The output of those 4 actions is well balanced because everyone can use them. Perhaps the power is best envisioned (systemically) as a really out-there stunt.
4b. Before you tie yourself up in knots "adjudicating" a power, consider just saying what happens. Magic can just be magic. A super-fast person can just be super-fast. That will create a situation that the other side has to respond to, which they will do...with the regular old 4 actions of Fate.
4c. This is not to say the 4 actions are sacrosanct. Definitely consider swapping one out if it fits your game. So long as it's A Very Small Number you're good.
5. Embrace the Pulp.
I don't mean the "pulp" gamers talk about, where there's like fedoras and Nazis and shit. I mean the actual meaning of the word in a literary history sense, where the emotions are broad and the plots are simple.
5a. NPCs should wear their Aspects on their sleeves.
5b. The setting should wear its Aspects on its sleeve.
5c. If you can't figure out how to make this happen, see 1 above. If you're doing (say) a Romance in the Air game and you keep making Aspects about the broader political situation that nobody can figure out how to call on then maybe the political situation isn't as relevant to the conflicts portrayed in the fiction as you thought. Maybe you need to think of a concrete, material manifestation of that political situation to be an Aspect. Or maybe it's just a background fact that isn't Aspect-ual at all. Not every fact that's true about the game world is an Aspect. An Aspect is just something that's directly relevant to the action of the action-adventure protagonists Right Now.