While trying to place a ring on the bulls obviously rubber horn, Don Manuel Arriegas horse is shown being gored in the right shoulder, with blood spurting out of the wound. In subsequent shots there is no sign of any wound. Additionally, many shots in the scene show lunges by the bull that would have disemboweled the horse had the horns been real.
During the bull - ring game, Glenn Ford is rolled on the ground, but when he pops up again, his clothes don't have a speck of dirt on them.
In a rail car containing the shipment of cattle, Tom Reese, an 'experienced' cattle-handler, attempts to help up a fallen steer by pulling the animal's head so that it can get up on its front legs then, presumably, on to its hind legs. No bovine will normally get up like this, and it's easier for it, firstly, to raise itself up on its hind legs by lunging forward, then put its front legs under it to stand up. To help this animal get up, you must lift its rear end by grabbing either the tail root or its backside.
While Don Manuel Arriega and Tom Reese are attempting to place the ring on the bull's horns, it is obvious the horns, which bend and flop, are made of rubber.
When Tom and Frank strike their deal in the hotel, Tom says "Get some sleep. We leave first thing in the morning." When Tom and the other cowboys arrive the next morning in the wagon, the shadows on the ground are very short, being almost non-existent. This indicates the sun is almost directly overhead and that it is close to noon, and nowhere near early morning.
The stampede scene had the cowboys using what appear to be 20th century model Winchesters with round barrels. They should have used octagonal-barreled model 73s.