Continuity mistake: When the Germanian leader is stabbed the first time he holds his weapon with both hands. When it cuts it's only in his right hand. (00:10:25)
Revealing mistake: In the shot after the Germanian leader get stabbed to death there is a Roman soldier and his horse falling to the ground. Look at the soldiers around him. They are moving unnaturally fast, like they are in fast forward. (00:10:35)
Continuity mistake: The weather during the battle against the Germanians changes almost every second: Hard snowfall, soft snowfall, almost sunshine, soft snowfall, etc. (00:10:35)
Continuity mistake: In the wagon, when Commodus gets up and sits down beside Lucilla, the sunlight coming over his shoulder changes between the shots. (00:13:00)
Continuity mistake: In the beginning when Commodus and Lucilla are talking and Lucilla says "For now, the first thing I shall do is have a hot bath." you can see she has her hand on her chest. When it cuts Commodus is suddenly holding her hand. (00:13:25)
Continuity mistake: When Commodus arrives and asks Aurelius if he has missed the fight, Aurelius' hair is blowing in the wind. When it cuts from behind Aurelius his hair is not moving. (00:15:50)
Continuity mistake: When Commodus tells Aurelius he will sacrifice a hundred bulls to honor his triumph, the snowflakes on his head differ between the shots. (00:15:50)
Continuity mistake: When Aurelius gets on his horse and Maximus is helping him, you can see Aurelius' arms are under his cloak. When it cuts to Aurelius saying "So much for the glory of Rome" you can see his left arm is uncovered. (00:16:30)
Continuity mistake: After the first battle when Maximus is washing his hands during the feast, you can see in the close-up of his hands that the wool sleeve on his left hand is thicker than in the other shots. (00:17:05)
Continuity mistake: When Richard Harris is talking to his daughter about her future, the fire lamp behind them changes positions between shots. (00:20:15)
Continuity mistake: When Aurelius says "Enough with politics. Let's pretend I'm a father." to Lucilla, she smiles and looks down. When it cuts she is still looking down, but in the next shot she is suddenly facing Aurelius again. (00:20:20)
Visible crew/equipment: After the battle with the Germanians, the next morning after the tavern, Maximus is walking in the army camp and he feeds a horse a piece of apple. If you look closely between him and the horse, there is a crewman wearing a pair of blue jeans. (00:21:00)
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)
Continuity mistake: When Lucilla says "Did you know, I still remember you in my prayers?" she looks up at Maximus with a serious face. When it cuts she is smiling. (00:28:35)
Continuity mistake: When Maximus is finished praying for his son and his wife, he calls for Cicero. We then see Cicero walk in to Maximus from behind while holding a cloth in his right hand. When it cuts he is holding it in his left hand. (00:30:05)
Continuity mistake: When Commodus goes to see his father thinking his father would pass his powers onto him, if you look closely when he enters, there's a white sheet blowing rather vigorously in front of the camera. When it cuts to a shot of Commodus, the sheet now is hardly blowing at all. (00:30:35)
Continuity mistake: When Commodus is holding Aurelius and says "Father.", he is holding Aurelius by the top of his head. When it cuts to a close-up of Aurelius looking up at Commodus, right before Commodus kills him, we see Commodus holding his chin instead of his head. (00:33:55)
Continuity mistake: When Commodus is choking Aurelius we see Aurelius placing his hands on Commodus' shoulders. When it cuts back to a frontal shot of Commodus the hands are gone. (00:34:20)
Visible crew/equipment: When Maximus is told the Emperor is dead we see him barge past Commodus to see the body. Look behind Commodus at the roof and you should see an electrical stage light. (00:35:00)
Revealing mistake: When the emperor lies dead he is clearly still breathing. (00:35:15)
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