Continuity mistake: In the beginning when Maximus says "Lean and hungry. Still nothing?" in which he gets the answer "Not a sign" from Quintus. Watch the soldier behind them handling the catapult. When it cuts that soldier is suddenly gone. (00:03:45)
Continuity mistake: When the Gladiators are fighting the Praetorians so Maximus can escape, they stab Hagen when he is on the ground. Notice that it is in a fast forward-like time. The Praetorians are moving really fast. (02:07:10)
Continuity mistake: During the first gladiator battle there is a shot of Hagen striking a man with an animal skull on his head. In the next shot sand is suddenly 'raining', from out of nowhere, all over Hagen. (00:54:25)
Continuity mistake: When Proximo is talking with the slave dealer and he says "You sold me queer giraffes, I want my money back.", you see him holding a cup with his index finger pointing up. When he takes a sip from the cup his finger is down. (00:46:35)
Visible crew/equipment: When Maximus has killed the tiger you can see a whip hitting it as it lies on the its back. It probably belongs to the lion tamer who tries to make the tiger wriggle. (01:42:05)
Revealing mistake: When Maximus is dying and entering Elysium, you can see that it's not Russell Crowe walking through the fields to his wife and son. The stand-in's build and physique is totally different. (02:19:45)
Continuity mistake: When Commodus is standing over his nephew Lucius, touching his face while he slept, his sister Lucilla enters the room and you hear only her footsteps, but he is then standing at the end of the bed out of reach of Lucius. He does not have time to make that move. (01:12:30)
Continuity mistake: During Maximus's death scene at the end you can clearly see the entrance that Commodus and Maximus entered the arena through in the floor of the arena. After Juba is done burying the figures of Maximus's dead son and wife, you can not see the entrance anymore when he is walking away. (02:21:00 - 02:22:55)
Factual error: During a meal in the gladiatorial school, Juba is shown eating with a metal spoon. Slave-gladiators almost certainly only ate with their fingers, wooden spoons, or wads of bread to sop up their food. They never would have access to metal spoons that could be sharpened and used to attack the guards keeping watch over them. (01:36:20)
Continuity mistake: After Maximus's family is killed and he is being taken away, he has flashbacks, but one of the images is of him being chained up against the wall, right before his final battle with Commodus - a scene which hasn't even occurred yet.
Continuity mistake: When Proximo gives Maximus his armor the horses have wings. After that they do not.
Continuity mistake: When Maximus stabs Commodus in the neck, in one shot we see his whole neck, and there's no knife in it.
Revealing mistake: In the beginning during the war with the Germanians when Maximus falls off his horse you can see that it's not Russell Crowe but a stunt double. (00:09:55)
Continuity mistake: When Proximo is about to be killed and says "shadows and dust", the background scenery changes. It is obviously an alternate take from when he says the same thing before Maximus fights Tigris, used because of the death of Oliver Reed, but that doesn't make it any less a mistake. (02:12:15)
Continuity mistake: After Maximus comes out of the tunnel after leaving the gladiator quarters, he sees his friend Cicero. Maximus makes a bird noise to get his attention, Cicero sees him and in an attempt to warn him he yells "Maximus." He startles his horse which runs away but a noose is around his neck so he is pulled off the horse and left hanging there. As soon as the horse leaves him and he starts swinging his hands you can see they are not tied. Then when Maximus runs up to him and holds his feet up to try and save him his hands are tied up. (02:12:50)
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: 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 Maximus pulls a knife out of Commodus' neck, it's much smaller that it was before.
Revealing mistake: When Maximus and friends are viewing the Rome Colosseum for the first time, the video raises to show the full length of the Colosseum. At the top birds are flying over it but some fly and disappear into nothingness. (01:18:44)
Other mistake: When Proximo says "Use this" to Maximus and throws him a piece of body armor, it is not the same armor he uses in the scenes that follow. (01:10:00 - 01:12:55)
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