Near the end, when Bess is in the empty theatre, begging Harry not to do the trick, she is clapping. You can hear the loud claps, although she is wearing gloves on both hands. You would never hear the claps, only muted thuds.
Newspaper editor looks over layout for "whatever happened to Houdini?" article, then assigns a reporter to go out and investigate the story. This is absolutely backwards - a story of such a speculative nature would always be written first, with layout following after the fact.
In the clip when Houdini is in London demonstrating his escape from a trunk, he gets 2 sailors to check the trunk. On the sailors' blue collars are stars. The Royal Navy did not have stars on their collars.
When the Houdinis and the reporter are being driven to the séance, the same rear projection loop is continually run in the car's back window, repeatedly showing the same background traffic, with the splice where the loop begins plainly visible each time.
When Houdini is doing the "levitation" trick on the stage, watch as Tony Curtis passes the hoop around Janet Leigh's body: twice you can see the split in the hoop "catch" on the lifting frame behind her body.