When the sanitarium guard interrupts Gravelle's piano playing, the guard slaps a newspaper down on the corner of the piano closest to the camera, to Gravelle's right. The guard moves away, and there is a cut to follow him. Then there is a cut back to Gravelle, who is still at the piano - but now the newspaper is centered directly in front of him.
When Charlie Chan is questioning Kitty she says her father died in a fire when she was 4 years old. That event is referenced as 7 years ago several times in the film so Missy would now be 11 years old but she is now speaking permission to marry and is clearly older than 11.
When they characters are all gathered in the dressing room after the murders and they are questioning Childers, he says he knew Madame Barelli well. What he actually meant to say Madame Rochelle (or Madame Lilli as she was being referred to).