
Revealing mistake: When the chariot crashes in to the gladiators, we can see the shield in which the chariot crashes in to. It's not shaped like the other shields which are shaped in a perfect bow. This shield is rectangular shaped most likely to balance better on what ever is supporting it when the chariot runs over it making the chariot tip over. (01:30:00)
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