According to my film history prof, Dr. Strangelove's hand was actually supposed to be mechanical -- making Strangelove a form of half-man half-machine and reinforcing the out-of-control technology theme. (I'm guessing this information is from the Peter George novel on which the movie is based, since it is not apparent in the film.) Thus the resemblance to the "alien hand syndrome," an actual affliction that can be caused by a stroke or other brain injury causing damage to the nerve fibers that connect the two brain hemispheres (the corpus callosum), could be purely coincidental. Strangelove's character is sometimes said to be a blend of Henry Kissinger, Edward Teller, and Herman Kahn.

from classnotes; description of the "alien hand syndrome" taken off