When Matson appears in the mezzanine, behind the candelabrum, he has his arms by his sides. In the following shot, his right arm is raising the gun.
Joe falls into the river with a lit cigar in his mouth. When he comes out, the cigar is still lit.
When Zack puts the money bag on the fallen stagecoach, Joe's muffler turns around his left shoulder between shots.
When Chad enters the room to invite Jarrett to lunch, Joe grabs his hat and holds it with his hand inside. Later, as Zach and Joe are heading to the bar, Joe stops to grab his hat, remarking Zach would understand why, indicating the gun he carries in it. The camera shows a glimpse of the inside of the hat, however, and no gun is visible.
When Matson falls from the mezzanine and crushes the table, his hat rolls away from his head. After that, the hat appears held around his neck.
When Zack and Elya are having lunch in the restaurant, there is a shot of a server carving roast beef on a cart. It is evident that the "steam" rising up to indicate that the roast is hot is not coming from the meat, but is instead special effect smoke rising up from in front and off to the side of the meat.
(at around 1h 20 mins) The movie is set in 1870. Joe Jarrett raises a mug that's marked on the bottom: Wallace-China-Los Angeles-California. According to Potteries of California, the Wallace China Company operated from 1931 to 1964.
At the Riverboat Casino opening, there is a jazz band playing "When the Saints go Marching In". Jazz and "Saints" did not appear until after the 1900s.
Early in the movie, when Joe Jarrett is riding away on his horse, there is a white car in the distant background driving from right to left. It comes out from behind the big rock on the left lower corner of the screen.
When Jarret and Angel come down the stairs, there is a bird cage with a flight cockatiel. That mutation is called whiteface. That specific mutation first appeared in 1964 in Holland.
When the riverboat is completed, it's shown flying a brand-new U.S. flag, but the flag has 50 stars instead of the 37 stars it would have had in 1870.
After the stagecoach wreck in the desert, as one of the principals is speaking to the others, in what should be a pristine desert background, a passing car is briefly visible at center screen left.
When Matson is first talking to Burden about the attempted robbery, he says he lost 6 men. In the shootout, he lost 8.
When Joe is hiring men to work on the boat, Angel should have recognized Pete Mancini (Richard Jaeckel) as one of Zach's men and should have turned him away. [Mancini helped Chad (Mike Mazurki) identify Joe when he came to Galveston, so early in the film it was apparent that Mancini was working for Zach. As savvy as Angel is, he should have known it.]
The organ has no pipes and an electric organ didn't exist in that era. It is a reed organ, as most were.