First, put me in the "I like this book but I wish there was more to it" camp.
To echo other poster's comments, the medieval childhood stuff was very helpful to me since I have not invested a lot of my hobby time into that area of study. I love the fact that Ars authors actually do some good research instead of making it all up out of whole cloth. Kudos to David and his team!
Of special note, though, are the Turbulences. I'm not big on rolling dice when decent storytelling and role-playing can do, but while I wasn't one of the playtesters, I would say that it is a great mechanic and provides a good foundation for why Hermetic magic leads to Twilight and other magic leads to different Warping experiences. The fact that it points out the danger of apprenticeship in something as risky as the study of magic without absolutely ruining a character before they even "graduate" I think was particularly brilliant.
As for teaching Virtues and so forth, I think the mechanic -- in and of itself -- makes sense, but I would suggest as others have for the players to give it some more thought than simply running the numbers. Gaining or transforming a Virtue during training has immense story potential and, assuming the players want to game it out, it shouldn't be wasted in the same way (as intended, I think) that a Mystery initiation should never be. I suppose one could go through an initiation for a Virtue in a Mystery by declaration ("Um, yeah. Steve, you are right, the mystagogue is powerful enugh to confer the virtue. OK, after the Spring season your character has it.") but I would much prefer a session or three where the the storyguide has already made sure of the 'accounting' and we play out discovering the secret cave, outwitting the guardian, making The Choice, suffering The Sacrifice, and Discovering the Greater Capability.
In a similar vein, playing the child terrified and alone in a new town with strange things happening around you all the time would be a lot of fun. For a year, you are forced to learn a new language that sounds like that used in the church services that you used attend from an old cantakerous clerk who doesn't like you no matter what but who himself is just as scared as you of the Master of the House. But to make it more fun, a year later the Master of the House (whose name, you discover, is Ignis of the Flabeau family) shows up and has a particularly nasty and creepy smile on his face and says, "It is time, come with me." You run for the door, but he barks a word and you are strangely frozen. Scared out of your mind, the candle flames around the room suddenly glow 10 time brighter. THe Master "tsks", waves a hand and flames die back. He looks at you with that same nasty smile and begins waving his hands and, as he does, the ssmile changes to a look of reassurance and the fear washes away over two minutes. The door to the room you were told never to enter now opens and you see a door made, you swear, of golden light on the opposite side of the room. He gently grabs you by the hand, and you both walk through where, over the course of the next three months, he leads you along a path where people and animals made of flame ask you challenging questions, or wrestle you, or give you odd challenges, with the Master occasionally coaching you (and quietly cursing a mistake HE made). On one occasion the Master said "Oh no, I'm not making the same mistake my teacher did," and personally stabs a flaming wolf in the side, killing it before he bit you. While you got a couple bad burns from the whole experience (and a personal disgust with plants), you did pretty well and sometimes very surprisingly. You return from the golden door at the end of the season looking at the world and language in a very different way and having a new and VERY special understanding of fire.
Playing each step in the Opening of the Arts could fill several sessions if you wanted and the mechanic just provides a reasonableness test as with the Mystery initiation mechanic. Could the mechanic be abused? Sure, if you let it. Can it be gotten around? Of course, but why would you?
Finally, if there is one complaint that I have, it is common one -- I wish there was more to it. But I still am very much liking the book and would ask that the authors and the editor take it as encouragement to push a little harder for more detail, more examples, and maybe a little more storytelling on thier own part in the future.
Well done (and sorry for my own weak writing).