Factual error: Here's a big historical mistake. The character of German Admiral Lütjens is depicted overall in this film as a wild-eyed Nazi fanatic. In real life, he was distinctly anti-Nazi, vehemently protested the anti-Semitic actions of Hitler's regime, and was himself subject to intense Nazi scrutiny as he was a quarter Jewish and his wife was half Jewish. He was one of many German naval officers who fought only for their country, not Hitler.
Factual error: The weaponry of the Romans and their use is wrong (as they are in all Hollywood movies playing in the Ancient Mediterranean that I know): Instead of one spear, each legionary would carry two weighted javelins, called Pila (singular: Pilum), which had a long narrow iron head. The purpose of these were to throw them at the enemy before melee; if they did not kill their targets, the pila would get stuck in their shields. The head shaft would bend, making the pila useless for 'return' to their original owners, and with the added weight of the javelin, the enemies' shields were rendered useless as well. Following this, the Romans attacked with short swords (the Gladii; singular Gladius).
Continuity mistake: Watch for the varying hairstyle of Mrs Brady in the scene in which Rachel comes to complain to her that her husband is a fake.