Revealing mistake: In the opening battle, it's quite obvious in close-up the arrows shot by the ballistae (war machines) can't really be travelling more than a few yards at most, not the great distance they're supposed to be flying and which real ballistae could manage.
Continuity mistake: In the Gladiatorial fight scene in Morocco, Maximus throws one sword with his right hand into the stand, still holding a sword in his left hand. The next instant long shot of him shows the remaining sword in his right hand as he taunts the crowd with "Are you not entertained?"
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