Conservation of angular momentum does not predict that the disk stays motionless, because the field in this case has angular momentum. The charges produce an electric field, and the magnetic field is not parallel to it, so there is a Poynting vector going around in circles, and the field angular momentum is just converted to mechanical angular momentum when the magnetic field disappears. The motion of the disk is required to conserve angular momentum, since the angular momentum would otherwise be radiated out in the radiative field when the magnetic field collapses, and in this case, some of the angular momentum is absorbed by the disk.
Feynman includes a version of this puzzle in the Feynman Lectures Vol II, and resolves it. The one thing he doesn't emphasize is that field momentum and angular momentum are conserved during slow changes without regard to the radiative field, which is not excited.
EDIT: On Parity with B fields
Reading the comments, it seems that you are concerned that the disk spins one way with one sign of charge, and spins the other way with the other sign of the charge. This looks strange, because the B field is completely rotationally invariant around the Z-axis and so is the E-field (assuming the point charges are small and dense), and it looks weird that the thing can spin in one direction--- how does it know to go one way and not the other?
The reason is that when you are thinking about parity (why one direction and not the other), the B vector is unnatural. The B-vector has a right hand rule in defining how it is made and how it acts. It looks like it violates parity, but when you use the right hand rule twice (once to make B and once to make a force), the result is invariant under parity. But the pictures look like they give weird unphysical forces. This is true for all B-fields--- even the B field making circles around a current carrying wire. How does it know to go one way and not the other?
The easiest way to resolve this is to draw the B-field not as a vector, but as a little swish, a swirl, in a plane perpendicular to the B-field direction. You should think of B (for parity purposes) as really living in the plane perpendicular to the B-field, and swirling in a certain direction. For the case of the disk, the B field coming up out of the disk is not really coming up at all, it's coming out in a swoosh twirling counterclockwise in the plane of the disk. This is reflecting the physical motion of the charges in the plane of the disk that give rise to the B-field in the first place.
The swooshing of the B-field removes any confusion regarding the sign of the rotation of the disk. When you add an E-field from surrounding static point charges, you generate field angular momentum because the pointing vector makes the B-field swooshing into an actual momentum flow with a definite angular momentum. This is where the angular momentum to spin the disk comes from.
You asked for a reference in the comments. The reference is Feynman lectures Vol II, where he discusses a circle of charges making a ring around a wire, and uses it to motivate field momentum and angular momentum. I forget the details, but it's the same sort of puzzle. These things were discussed in the late 19th century, when field momentum was discovered. Maxwell, Hertz, Pointing, Lorentz and other contributed, but I didn't read this original literature, since resolving Feynman's puzzles using modern formalism gives you the content of this literature most quickly.
Feynman often gave puzzles of this sort to summarize old and forgotten literature for a modern audience, to keep it alive. This was a wonderful service he did to previous generations, and it is one of the reasons he is so revered not only as a researcher but as a teacher. The puzzles are each really deep questions of a previous generation of physicists.
(a) As far as I know, Faraday's law in electromagnetism is another name for Faraday's law of induction.
(b) You refer to the equation $$\vec{\text{curl}}\ \vec{E}=-\frac {d \vec{B}}{dt}.$$
Applying Stokes's theorem (and taking the differentiation outside the integral sign) this integrates to $$\oint \vec{E}.d\vec{s}=-\frac{d}{dt} \int_S \vec{B}.\vec {dS}$$
The left hand side is the line integral of the electric field, that is the induced emf, in a closed loop enclosing an area S, and the right hand side is the rate of change of magnetic flux through S, so we have $$\text{emf in loop = –rate of change of flux through loop.}$$
So the difference implied in your second paragraph between the curl equation and "emf = – rate of change of flux" isn't a difference at all!
(d) All this is valid whether or not there is a conductor.
The betatron is a particle accelerator that can be understood in terms of an induced emf in a non-conducting toroidal chamber. You could argue, I suppose, that the presence of electrons being accelerated in the chamber makes it a conductor! But it would be weird, wouldn't it, for the emf suddenly to appear when electrons are injected into the chamber?
(e) The equation "emf = – rate of change of flux" can, though, also be applied to a moving conducting loop cutting flux, though this time the emf arises from magnetic Lorentz forces driving charge carriers around the loop.
Best Answer
Feynman meant that conservation of energy always holds, so that if you have a static situation, the force field on a particle is conservative. For magnetic forces, you have moving (and changing) currents in the solenoid, so its not static, and if you extract energy from the field, you just weaken the current and extract energy from the system producing the field, doing work on it.
The fact that magnetically induced EMF is non-conservative is the basis of countless claims of perpetual motion machines, so it is good to say early that you can't do this.
Magnetic fields that are changing give rise to non-conservative forces, the integral around a loop is the change in flux inside, but the process of extracting energy from the EMF reduces the magnetic field, and the amount of energy stored in it.
Feynman discusses transformers and the EMF around a loop. He also discusses something else even more counterintuitive and not at all discussed by other people. He shows two moving charges, A and B, so that A is moving perpendicular to the line joining A and B and B is moving along the line joining A and B.
In this case, the force from A on B is not equal and opposite to the force from B on A! This shows you that the (nonradiative) field is carrying momentum, and is transferring momentum to the two charges as the E and B fields rearrange. The recognition that you need to include fields in the conservation laws was long in coming, and this example is just as useful as the transformer for explaining this. Feynman also discusses a case where the field is carrying angular momentum, a collection of charged balls with a current, and when you switch off the current, the balls start to rotated around.