The opening scene shows King Stephen being held in a squalid cage in Lincoln Castle. In fact, he was held prisoner in apartments in Bristol Castle, hundreds of miles from Lincoln. Though at one point he was chained, he was far too high-ranking to be caged or left in filth.
Matilda tells her son Henry (the future Henry II) that she is now Empress because "I rechristened myself this morning. One day you will be Emperor". In fact, she had legitimately acquired the title Empress nearly 30 years prior, when she married the Holy Roman Emperor Henry V in 1114 and ruled the Empire with him until his death in 1125.