The amount of grape soda in both Claire and Miles' bottles increases in subsequent shots after they've had a few drinks of them.
Claire keeps referring to "Occam" (or Ockham) as the author of "the principle of William of Ockham's Razor". So it was actually William who lived in Ockham, Surrey, England. It actually goes back all the way to Ptolemy & Aristotle. (Shakespeare also quoted it.)