Unfortunately I haven't actually watched a Passion of the Christ, but I will be able to go into (gory) detail about what happened before a crucifixion. Someone who is going to be crucified is tortured, for multiple reasons.

Before a crucifixion, flogging ('scourging') would legally have to occur [1]- only women and senators would be exempt from this. How the victim was flogged varied, usually you would be flogged with a short whip, and upon the leather, there would be pieces of animal bone, or even iron, tied on, for even more pain. The victim would have his hands tied to a post, naked, so he would be in an upright position, and the scourging would occur on his bottom, legs and his back. It would, in most cases, be severe, carried out by one or two people, until the victim was near death or in a state of shock [2]. The victim would end up with serious wounds and contusions, the muscles in the back and legs would tear and there would be serious blood loss. The victim would essentially look like his back was torn to ribbons- I can't overstate how damaged his body would be, or how cruel a scourging was. Soldiers would often taunt, curse or laugh at the victim [3], who by then was in a state of medical shock due to the pain and loss of blood, but this wasn't legally required, unlike the scourging. This would definitely have happened to Jesus before crucifixion, and I doubt any film could accurately portray the pain and damage it would cause, but I seriously doubt that, if a flogging is portrayed before a crucifixion, Mel Gibson exaggerated this torture. By the end, the victim would struggle to even make sounds, or moans of pain.

Why would they do this? In your question, you asked about the torture if someone was already going to be crucified, and your answer to why is in that question. Crucifixion was a painful, slow and torturous death and therefore only reserved for, who the Romans considered, the worst of the worst [4].To die and suffer in full view of everyone, to be taunted by a crowd as you breathe your last, would be seen as incredibly shameful- and that was how the punishment was meant to be seen. Crucifixion was designed to be as degrading and shameful as possible for the victim, and adding in a level of torture, through scourging, was therefore 'ideal'. This was why crucifixion was so rarely used for actual Roman citizens, because of how shameful and cruel it was seen to be- unless you were a soldier who had deserted, that was.

It was also customary for the condemned man to carry the cross from the flogging post to the site of crucifixion- outside of the city walls [5]. As mentioned before, the victim would be in a state of shock, bleeding out and unable to even make full sentences, and still naked, so to say the victim himself carried a full cross would be to state the impossible. Crosses were very heavy, weighing approximately 150kg, and therefore the bar of the cross (if this is the cross, +, then - is the crossbar) would be what the victim actually 'carried' [6], balanced across his shoulders, with his arms then tied to the bar. He would have walked dazedly and may have needed support from the soldiers just to reach the point of crucifixion. This was another way of shaming the victim. To shame the victim, along with the crowd taunting him, a sign with the man's name, crime and, sometimes, status, would be carried by a soldier in the small procession surrounding the condemned man's walk to the site of execution. If I was a slave, who had been accused of the murder of my owner and his family, then my sign could say '[Name], 'murder of master and family', slave' for example [7]. In the case of a free man, such as Jesus, he likely only had his name and crime on it. Before the cross was set up for crucifixion, this sign was placed upon it, so when the cross was set up and the victim crucified, all who saw the site knew of the victim and his crimes. Then the Roman guard would wait- and wait. The last thing the victim would probably see was a small group of guards, and the last thing he'd hear was probably taunts or even just general chitchat from the, probably bored, guards, who would wait until they were absolutely certain the victim had died. This could happen very quickly or very slowly, depending on the cruelty of the scourging, the physical state of the victim before the scourging had took place and even the weather [8].

I'm presuming he was shown being nailed to the cross? This May or may not have happened, it is not completely unrealistic. After being given some myrrh and wine [9] (isn't that strangely sad? I'm not a Christian, but to think he was supposedly given myrrh at his birth, and was given myrrh just before his death is quite depressing), this would numb him, essentially a crude pain reliever. It was cheap and would not numb the pain completely, however.

Depending on where you were, you would be nailed or tied to the cross. I'm not sure of the practices in the place Jesus was executed, although usually victims were nailed to the cross, in some places, tying was the preferred method [10]. Nailing added another level of pain and misery. They'd be driven through the wrists and were probably up to 1cm wide at the tip- and even up to 20cm long. They would have stuck out of the wrists but would have held the gictim firmly in place. Although we call these 'nails', they are more like the metal spikes you can see on fences. The feet would suffer the same treatment- nails, or spikes, through the ankles usually.

The torture would not stop once the victim had been crucified as the law dictated. Some soldiers would break the victim's legs below the knees- this hastened the death [11]. It could be considered an act of kindness as it would undoubtedly speed up the death, but it would add another layer of helplessness and shame, which was exactly why the torture was carried out. The crowd and soldiers would taunt, jeer and curse. Death could happen in hours- or days. Insects would sometimes come to burrow into open wounds, birds of prey, such as vultures or eagles, may even have attacked the victim while s/he was still alive [12].

The torture probably depicted would not have been exaggerated in how excruciating it would have been, or how humiliating, although the methods may well not have been accurate.

So to answer your question by rephrasing it as what general misconceptions are there about the crucifixion of Jesus, I would say that, firstly, Jesus should not have been depicted carrying a full cross, instead just the cross bar, that Jesus was unlikely to have been whipped with sticks of thorns (as he is sometimes depicted as being subjected to), rather a short whip with bone or iron embedded in the leather, and Jesus would have quite possibly have his knees broken (often by using metal clubs) while or before being crucified.

[1] A History of Rome, the Establishment of the Empire, Henry George Liddell

[2] Crucifixion in the Ancient World, J Med1995, M Hengel

[3] Execution by crucifixion: history, methods and cause of death. J Med1995, JE Holoubek, AB Holoubek

[4] Public Executions: from Ancient Rome to the Present Day, Nigel Cawthorne, pg11

[5] Ancient Jewish and Christian Perceptions of Crucifixion, David W Chapman, pg 96

[6] Crucifixion in the Ancient World, JMed1995, M Hengel

[7] Spectacles of Death in Ancient Rome, Donald Kyle, Pg 183

[8] Skeletal remains from Giv'at ha-Mivtar. Israel Exploration Journal, 26, 35-38, V.Moller-Christensen.

[9] In the Fullness of Time, Paul Mieir, Pg 50

[10] In The Fullness of Time, Paul Mieir, Pg 165

[11]The Crucifixion of Jesus: A Forensic Enquiry, Frederick Zugibe, Pg 105

[12] The Crucifixion of Jesus: A Forensic Enquiry, Frederick Zugibe, Pg 53.