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In the series, and thus, the official explanation in continuity, the cause of Grievous's cough is: Mace Windu uses the force to damage Grievous's internal organ sack (brought up again in Episode III).
Series producer, Gendy Tartakovsky revealed in his Hyperspace commentary on starwars.com and on the Volume I DVD that he purposely animated C-3PO with eyes that sort of move around to pay homage to the animators of and the animation style of Nelvana.
The series will be realized as a 3-D computer animation project created by the new Lucasfilm Animation division in their Singapore and California locations.