Keep an eye on the scenes involving Moto's second trip into the swamp in the latter half of the film. The lower half of Mr. Moto's pants are alternately muddy and clean in scenes that take place at the villains' camp.
Mr. Moto and Twister obtain a mud sample from the swamp and place it on a canvas bag laid out on the deck of the boat. But when they have to pull away in a hurry under gunfire, the canvas is there, but the mud is gone.
At 28.35 a valet enters Moto and McGurk's room asking if McGurk wants his bath run. He replies he had just had a shower. Moto says he can run his bath. Seconds later the valet is killed when he touches the tub which has been wired to electrocute anyone who touches the pipes.
The names of the newspapers whose headlines are shown all refer to 'Porto Rico'. This anglicised version of Puerto Rico's name was indeed used by English speakers (and by one newspaper, the Porto Rico Progress) after the Treaty of Paris in 1898, but Congress changed the official name back to Puerto Rico in 1931. Hence the newspapers' names would be clearly incorrect in 1939.