Even if they are possible within the current system, they are broken.  Virtually everyone who has GM'd a game with them says so.  If you want to use them, there are ways to do so that do not break the game.  Please see the above suggestions.

Outside of those, I do think Magic is still a little unbalanced.  I think you simply get too much with spellcasting.  Enchanted Items are extremely strong, especially defensively, if focused on.  Foci+Specializations+Skills all adding to a single roll is more than any thing else in the game, making magical attacks the strongest.  In play, it's often not too bad, but you tend to see well build spellcasters punching a few steps above their weight class.  I have a houseruled system that I think fixes all of this and have used in Fate Core versions of the game. 

That being said, I think the RAW system works pretty well.  Its balance issues are not horrid and can be planned around if they crop up.  We didn't really see a problem with them for quite a while, and some custom powers for the non-spellcasters fixed things nicely.  The fact that I like the system doesn't stop me from trying to improve it (especially to my groups' particular tastes), which is a sentiment that I think Sanctaphrax echoes.

Here's how I ran mental attacks:
In order to make a mental attack, you had to invoke an appropriate aspect on the target.  So for most mental characters it meant that they were making the attack every other turn, or spending fate points to keep invoking (limiting the amount of damage they could do).  If I were doing it again, I'd probably change the mechanics a bit.  Instead of Accuracy+Weapon like a normal attack evocation, I'd make the attack roll equal to Power with a Weapon 0.  But that's because I don't want mental toughness to become a "must take" power for everyone.

The two things that are a bit too strong are Evocation (foci and specializations stacking, control bonuses adding to attack rolls) and enchanted items. 

Ultimately, they're not too overpowered, but they're stronger than almost anything else in the system.  They don't break the game, or make playing other types of characters un-fun though.

Skill shuffling is also a bit broken, on the non-magic side.

I really like the idea of it being a non-military, non-intelligence organization.  It keeps it away from the normal power structures of government (how many presidents are about libraries, or even the IRS's day to day operation).  It also helps keep things away from escalation of firepower.

For as to how they operate, I take a page from Warehouse 13 and "The Librarian" and its sequels.

Also, make the British Museum antagonistic allies (i.e. the British Museum still assumes it has jurisdiction over this sort of thing for the ENTIRE PLANET).

Before I had to drop out of the playtest, I got to see the first document.  They have an interesting new mechanic that essentially divides characters into tiers.  Magic allows a character to perform an action at a higher tier.  Success and failure mean different things when different tiers interact (so you can't shoot Mab in the face and kill her).  It needed some work, but I'm really excited to see how it finally polishes up.

Casting didn't involve stress, but a different mechanic based around the FP economy.  And I think that's all that can be said without violating the NDA.

When you don't have the stress to take a hit, you're taken out.  Consequences are a way to avoid this, but they represent an advantage your enemy can use (free tag when they inflict one).  They can also be compelled by the GM, like any other aspect, but given their nature these compels are often more negative than others.

I'd just make them an aspect. Spend a fate point to invoke.  They don't come up that often.