This slipup can be noticed in the Battle of Carthage reenactment. Maximus and the rest of the "barbarian horde" are armed with spears and shields. The enemy chariots each have a driver and an archer. Then, near the climax of the battle, Juba throws Maximus a sword out of nowhere! That was very strange.
All the Roman Soldiers would have been fully armed, ie they would have the sword and most likely a smaller weapon as well as their main weapons. Basically there would have been hundreds of weapons strewn around, including the Rudius swords.