When Jack lifts the head of the dictator in the freezer to do the make up - you can see on the dictator where HIS make up, darkening his complexion, ends by his ear and on the neck.
When Ralph (Jonathan Winters) meets Simms/Jack (Richard Dreyfuss) after the TV speech recording, he asks to use the president's bathroom. Simms gives him the direction "one left, one right, two more left". But as Ralph exits the door, he turns right instead of left.