When Houdini returns to the stage after the safe trick at the Adelphi Theater, the large stop watch on stage is stopped yet the hands change positions between shots.
The private show for the Kaiser never took place. Moreover, had any "expert marksman" used the musket, they would have noticed the difference between a "live round" and the blank fired at Houdini. The recoil on a blank is far less than a live round.
In his private performance for Tsar Nicholas II of Russia, Tsarina Alexandra speaks with a Russian accent. The real Tsarina Alexandra was born and raised in Germany and never fully learned to speak Russian, she instead spoke her native German and thus would not have had a Russian accent.
In Houdini's private performance for Kaiser Wilhelm II, he asks a German Army officer to fire the rifle in his "catch the bullet" trick. The officer gives his rank as Oberstleutnant, which translates as Lieutenant Colonel. However, Houdini addresses him as "Lieutenant," which is several ranks below that of Lieutenant Colonel. Furthermore, "Lieutenant Colonel" is never shortened to just "Lieutenant," if shortened it is shortened to "Colonel."
When Houdini meets with the secret service in London, the man introduces himself as the head of the British equivalent of the US Secret Service, and says the name MI5. MI5 was only officially given that title in Sept 1916. It would have been called the Secret Service Bureau at the time this meeting with Houdini is portrayed to have taken place.
When Houdini visits the office of the government official in Washington, there is a U.S. flag on stand. It has 50 stars.