1) As one planet moves around one of the stars in a double star system, the side of the planet which is illuminated by the nearest star does not follow the nearest star as seen by that planet.
2) Two different planets in identical orbits around the two different stars are illuminated identically. They shouldn't be.
The above picture illustrates this problem.
The upper half shows the star system.
The bottom left image is of the planet orbiting the left-most star of the upper image.
The bottom right image is of the planet orbiting the right-most star of the upper image.
Both planets are vertically above their respective stars (at what I call the 0 degree position).
Catalogs and Cel:// URLs which illustrate this problem are in the Zip file
http://www.lepp.cornell.edu/~seb/celestia/confused_illum.zip
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