What causes the spokes of a Wagon Wheel to "move"(rotate) in the opposite direction of the Wagon Wheel itself? Is it my mind's eye that is the problem or is this a "artifact" of the film? I would think it was my mind's eye as the medium of film is purely analog and not a digital representation that exists to conform to "what should be" and not in fact what is visually seen.
This happens when the wheel is observed as an image through a projector or with light shining on it that is periodically blinking. What you are seeing is essentially the additive effects of two periodic functions, the first is the period of the light flicker and the second is the period of the wheel rotation.

So, if the wheel is rotating at a frequency that is evenly divisible by the frequency of the light, then the spokes appear to be standing still. If it is rotating faster, then they are appear to be moving in one direction. If it is rotating slower, then it appears to be moving in the other.

Under household lighting, the light pulses are at 60 Hz. The frame rate of movie cameras is usually 24 Hz.