Continuity mistake: The man on the left holds the cards with both hands in one shot but with a single hand in the following. (00:17:08)

Visible crew/equipment: The first time we see Fogg the shadow of the camera operator (film director?) and camera sliding smoothly along tracks is perfectly visible.
Continuity mistake: The position of Fix's hands changes between shots. (01:47:41)
Continuity mistake: The hull of the Rangoon boat changes from white to black.
Factual error: During the balloon ride the Basilica of the Sacred Heart of Paris is seen. It began to be built in 1875, 3 years after the date the movie is set.
Factual error: The Welsh Guards parading at the start of the film weren't formed until 1915. The film is set in 1872.
Continuity mistake: When the train in Mumbai leaves, the light keeps changing drastically in every shot.
Continuity mistake: The Mongolia ship on the Indian harbor (a set) is different to the one that sails the sea (a real ship), note the design of the hull and its rust stains.
Revealing mistake: When the ship is about to leave, in a close-up one can see the sky and clouds are a painted backdrop: no perspective at all, the clouds inches away and at waist level. (01:01:33)
Continuity mistake: The way Charles Boyer holds the postcard with the balloon picture differs between the wide and close-up shots.
Character mistake: During the military parade, check the lady behind the soldier on the left. She can't help stare at the camera the whole time before the soldiers arrive. (00:07:03)