Continuity mistake: When Ponty's rival asks at the board meeting "May I ask a question?" the man with the cigar is smoking it, and then just holds it in his hand next. (01:37:25)
Continuity mistake: During the board meeting, watch the moment when Ponty namedrops Dr. Kildare. Mr. Bratt is a couple inches away from him, but in the reaction shot looks like he's sitting far away from him. (01:38:50)
Continuity mistake: When JB talks to Ms. Jones on the intercom after talking to his wife on the telephone, he asks where the "You know" is. She says "It's in your top right-hand drawer." You can see him moving to his left.
Continuity mistake: When Finch first gets the job at World Wide Wickets, he asks Bratt to light his cigar. The shot then changes to Rosemary and her friends, and when it comes back to Finch, the cigar has disappeared.
Suggested correction: Actually, no! His left hand is not in frame anymore, but he is looking at it with a "What am I gonna do with this thing?" expression. And even after a long while and a lengthy cut to the president's nephew, at the very end of the scene when Finch says bye to Rosemary and her friends, he's specifically shown holding the cigar as he flips through his book.
Continuity mistake: J.B. Biggley at the elevators realises he's going to be blackmailed by his nephew Bud Frump. Bud's hands change position on the suitcase throughout the scene.
Continuity mistake: During the crescendo and ending of "Gotta stop that man", the towel rests on Finch's upper arm and shoulder differently in different shots.
Continuity mistake: Finch gets inside Mr. Bratt's office. Meanwhile, Rosemary has brought her friends over, and they watch him come out of the office as a new employee. Throughout the scene, the people in the background change without consistency between camera angles.