When Duke (Bing Crosby) is playing cards at the start of the movie, the number and position of the cards changes between shots.
The lead characters repeatedly talk about being in Alaska after they've crossed over the border into Dawson City, Canada.
When they first visit the Golden Rail saloon, Chester (Bob Hope) mockingly calls Duke (Bing Crosby) "Einstein". But the Yukon Gold Rush was from 1896 to 1899, whereas Albert Einstein first achieved public acclaim in 1905.
The right arm of the person holding the talking fish is visible.
When Sal is at Ace's saloon, she thinks he is a nice man who will help her. When she arrives at the mountain cabin, she knows that he is a villain. But there is no scene in which she finds out the truth and no explanation of how she knows.