Character mistake: When Maximus is talking to Marcus Aerelius, he mentions that his wife has black hair. But in the scenes where we see her, she actually has brown hair. (00:24:40)
Character mistake: Prior to the opening battle, Quintus says "The danger to the calvary" instead of "cavalry." (00:04:00)
Chosen answer: No, they are full brother and sister. They both had the same mother and father. Incest was not exactly normal at that time, but it stretches back within the imperial families as far as Caligula and possibly earlier. There is no evidence to suggest that the real Commodus was attracted to his sister, it was probably just included in the film in order to make the character seem more disturbed, and also as another reason why he would be Maximus' enemy (Maximus and Lucilla were, after all, once lovers).
The Doctor