When Harry and his wife are berated backstage by the father of the murdered girl they were attempting to channel on stage, the date was 1896. However there is a review from Variety on the wall. Variety began publication in 1905.
When Houdini is in a media scrum, some of the cameras, notably the Speed Graphics, were models unavailable in the twenties.
When Houdini is in the Hollywood screening room watching his appearance, a woman walks in front of the screen but there is no shadow thrown on the screen.
On the screening room wall during Houdini's 1922 visit to Hollywood is a poster for A FACE IN THE FOG (1936), a film which would not be made until after his death.
In London, when Houdini makes the elephant vanish, he violates a cardinal rule of magical performance: never announce ahead of time what you intend to do (it tips the audience what to watch for. keeping quiet adds suspense to the effect, and it helps you cover yourself if something goes wrong.)
In London, when Houdini walks through the brick wall, he violates another cardinal rule: never do a trick twice for the same audience (it's not a surprise the second time.)
When Houdini is going away to Europe, his mother says to him "Vielleicht, wenn du kommst zurück, werde ich nicht mehr da sein." This revealed her to be a non-native German speaker. 'Wenn' translates into English as 'if.' Some may say that she say "Vielleicht, wann du kommst..." This would also be incorrect as 'wann' is a question word. She also broke a very large element of German grammar that no native or fluent speaker would break. The correct statement for the subtitle translation ("Perhaps when you come back, I wont be here anymore") should be "Vielleicht, als du zurück kommst, werde ich nicht mehr da sein." Her pronunciation especially on the word 'ich' is also very strange.