After the bushwhacker is stabbed in the chest by the Indian girl, the leather strap for his leather pouch is up high around his neck with several inches between it and the knife blade where it's stuck in his chest, but the next time he is seen the leather strap is down right on top of the knife, even though he hasn't moved.
At about 11 mins in after Kris Kristofferson kills the road boss, you plainly see two "Oars" in the back of the wagon, and there is nothing in the boat whatsoever, as they "push off" in the boat you see they left the oars in the wagon! Then at about 12 mins you see them paddling away with paddles.
Jim Bowie threw his knife in camp at a distance of at least 20-30 feet and severed a rope, an extremely accurate throw. But the Bowie knife is too big and unbalanced for throwing, and could never be thrown accurately without wobbling off target and tumbling harmlessly. Jim Bowie was not a knife thrower, he was a knife fighter and his knife was a hand-to-hand fighting knife, not a balanced symmetrical throwing knife.
During the attack on Santa Anna's camp, one of General Sam Houston's officer's on horseback gave the order to "Forward, march!" However, the men charged. The order should have been to charge, not march, so the men didn't disobey, the officer gave the wrong order.
The blacksmith that is supposedly forging the red-hot horseshoe blank at the beginning of the movie right after the swamp scene, strikes the red-hot blank incorrectly and knocks off a big chunk from one end of it, yet he continues striking it as though nothing were wrong. The blank is ruined at that point and must be re-melted and re-forged.