Houdini's eye color changes from brown when he was a boy, to green as an adult. Even though his "American" passport lists his eye color as brown, there was no attempt to disguise Adrien Brody's natural green eyes.
The capital of Russia at the time of Houdini's visit was St Petersburg, not Moscow. Very doubtful he gave a performance to the Royal Family in Moscow.
The language of the Russian Royal Court was French, not English.
The men dressed in Civil War uniforms to fire the cannon Houdini is tied up in front of are wearing cavalry (horse soldier) uniforms, not artillery (cannon solider) uniforms. Cavalry used yellow trim, artillery used red.