Although the setting for the film is some time in the 1920s, as indicated by the cars and other details, Mark Weston is described several times as an agent of the "Federal Bureau Of Investigation", the FBI. It was not until well over a decade after J. Edgar Hoover took over the bureau (in 1924) that it became a federal organization. In the period of this film, it would still have been simply the Bureau of Investigation, a domestic arm of law enforcement which would be most unlikely to send its agents abroad.
When Maria Lieberson is branded by Fu Manchu's henchman, the henchman first spits on the supposedly red-hot branding iron, but no steam or smoke rises from the iron. Then, in the brief shot where he pulls the iron back from her flesh, her skin is clearly unmarked. Then, in the following shot, Maria's back shows a red welt from the branding iron, but it is much larger than would have been made by the iron used.
When Maria Lieberson is tortured on the rack, the ropes binding her arms are very obviously slack.
During the barroom brawl a waitress hits sailors over the head with her tray. She clearly does not connect any blows and the sailors have no reactions to being struck.
Nayland Smith mentions that he is going to Paris to discuss forming an international police body called INTERPOL. It wasn't until 1953 however, that the International Criminal Police Commission (ICPC) became commonly known as INTERPOL when it changed its name to match its telegraphic address.