When the old bull and young bull are fighting, the old bull is a Brahman cross bull, probably a beefmaster or beefmaster type. This is easily identified by the loose skin, particularly around the sheath, and slightly larger ears. However, the first Brahman cattle were imported into the United States in 1854 from India and were used in a circus; cattle for breeding were not imported until the end of the 1800s. These cattle were kept solely in the Gulf states until well into the 1900s due to the fact that they are extremely heat-tolerant but do very poorly in colder climates. Even today's Brahman and cross cattle could not survive in the extreme winter weather of the north. (See: American Brahman Breeders Association, History of Brahman Cattle) While this would be unnoticed by anyone who was not very familiar with breeds of cattle, it would never occur in real life.
After Cimarron calls Slim's Mom a name, and they fight, when Cimarron is getting on is horse to leave, you can see Slim putting his hat on in the background as he walks up. When the camera changes to a close up of Wil and the boys, Slim is standing behind him, and isn't wearing his hat.
When Mr. Andersen is in the school, he puts a mark for Belle Fouche, SD on the board. He states his ranch is here, 400 miles away, and he draws a line headed NW of Belle Fouche. This would place him about Lewistown, MT. It is doubtful that Mr. Andersen would travel 400 miles to Belle Fouche, when Bozeman and Billings are both much closer, and in dire need of beef. The first big herd of cattle didn't come to MT until after the war (1866) so there was no way that they would have taken them east to send them further east.
When Mr. Andersen is branding the calf during roundup, he only touches the iron to the calf once even though the brand on other livestock clearly shows two distinct O's. Before he brands the calf, one can clearly see that the iron is a single O.
It appears that the Double O ranch has two different brands. During roundup and later in the film, the cattle wear a brand of two distinct O's separated by about 12 inches. In the scene before they start the drive, one of the horses appears to have a brand consisting of two Os connected horizontally. This brand should be the same as the brand the cattle wear. In addition, the connected Os might be called a lazy 8.