A few points (I just joined to post this comment, and it's a doozy, so bear with me):

1. It's a common (and irritating) misconception that human dissection was illegal throughout the Middle Ages and Renaissance. From the 13th century onward dissections were regularly and LEGALLY carried out by physicians (well, directed by physicians, but performed by barber-surgeons). There were no explicit Church proscriptions on the practice. Granted, dissections were swift and smelly, and rarely gave onlookers the chance to really pry into human anatomy, but public dissections were nevertheless openly conducted. In fact, in 1315, the Italian anatomist Mondino de Liuzzi performed his first public dissection with permission from the Vatican.

2. Michelangelo had indeed dissected corpses (with Church permission) earlier in his career, although according to his 16th-century biographer Ascanio Condivi it made him sick to his stomach and he eventually gave it up for this reason. But if we're going to talk about Renaissance artist-anatomists the true distinction belongs to Leonardo da Vinci. Unlike Michelangelo, who really was only concerned with representing anatomically accurate forms in his art, Leonardo pursued anatomy with an engineer's eye for function. His voluminous notes and sketches, which he planned to turn into a magnificent treatise, include some extraordinary insights and innovative design schemes, some of which have only been recently applied to anatomical illustration. So tl;dr: Leonardo da Vinci was light-years ahead of his contemporaries when it came to anatomy, and certainly more expert than Michelangelo. Still, Leonardo had some inherited misconceptions...

3. ...one of which concerned the structure of the brain. Since Galen, physicians had regarded the brain as the seat of human intellect and the soul itself. Nemesius of Emesa, a 4th-century bishop, postulated that three cavities or "cells" in the brain (corresponding to the actual ventricles) controlled sensory perception and imagination, intellect, and memory by regulating the "animal spirit" (actually cerebrospinal fluid). Leonardo subscribed to this theory of cerebral cells, as his studies of the nervous system indicate. Example: http://www.unige.ch/cyberdocuments/theses2003/RivaraC-B/images/fig.1.jpg

The drawing on the left reflects an earlier stage in Leonardo's investigation - the cells are simplified and schematic. The right one was probably made after studying the ventricles of a large mammal (perhaps an ox) and then superimposing them on a human brain. The lateral ventricles are labelled imprensiva, so they govern sensory perception; the third ventricle is labelled sensus communis, so it governs imagination (the "special" sense); and the fourth is labelled memoria (memory - duh). It's a twist on the Nemesian theory that reflects Leonardo's strong belief that the soul resides in the sensus communis in the center of the brain. So tl;dr: neurological theory was quite developed by Michelangelo's day, if a bit off the mark. Also, Michelangelo would have been familiar with the ventricle/cell theory - it was cutting edge at the time.

Now, regarding the Creation of Adam.... I was a bit skeptical at first (still am), but I'm intrigued by the correspondence between the position of God and the position of the ventricles in Leonardo's drawing. God's arms roughly match the lateral ventricles, associated with touch. His chest maps onto the sensus communis, the seat of the soul. His legs and feet roughly mirror the fourth ventricle, devoted to memory - and our feet leave traces of where we have been before. Perhaps we should not be focusing on the anatomical details supposedly surrounding God, but on the anatomical significance of God himself in this scheme.

So here's what I think: if Michelangelo did this intentionally, which is still debatable, it was to indicate the divine source of the human intellect, residing in the ventricles of the brain, and the intimate connection between man and God, microcosm and macrocosm. We can't make the mistake of placing 20th-century anatomical knowledge in the mind of a 16th-century artist. But it does seem that Michelangelo wanted to make a point about God and the human mind/soul.