In the scene when Harry is dressing (shortly after his arrival in his Edinburgh hotel room) he starts to put on his braces (suspenders). In one shot they are partially unfastened but in the next shot (a close-up) they are securely fastened.
The opening scene reveals the partially built arches of the Sydney Harbour Bridge behind Houdini as he is lifted to the surface of the water. Houdini died in 1926. Construction of the arches did not commence until 1928.
In the scene before Houdini try to communicate with his passed mother via Mary McGarvie, it can be clearly seen there is a vacuum tube that happened to be a 6C33C Russian vacuum tube, which does not exist until the 60s, and further more, that vacuum tube couldn't work anymore, since it was leaked (it has a white layer of powder inside the tube that shows there is air inside).