Continuity mistake: When Mr. Ferguson is measuring the wax figures, he's shown holding a tape measure up against the figure of Landru (the one holding the rope). In the next shot, the figure is shown with no one near it. The next shot again shows Mr. Ferguson measuring the figure.
Continuity mistake: During their conversation over tea, Mr. McKenzie tells the Ransomes about the other people aboard ship. One elderly couple, the Whiteaways, are sitting in the background in almost complete shadow - until McKenzie introduces them. Then we see them in sudden brilliant light, and they've shifted their seating positions relative to the table. When we cut back to the master shot, they're back in shadow and back in their original positions.