Top 10 Ways that Mel's Passion Isn't As It Was, Number 4...

4. It wasn't blasphemy to identify yourself as the Messiah or the Son of Man.

The movie:

The climax [of the trial sequence] comes when Caiaphas asks Jesus: "Are you the Messiah?" and Jesus says, "I am..." and alludes to himself as "the Son of Man." There is a gasp; the high priest rends his garments and declares Jesus a blasphemer.
He was not, and Caiaphas never could have credibly claimed so.

The term messiah is the Hebrew equivalent to the Greek word christos (shortened to Christ for Jesus). Both mean "the anointed one," someone who has been set aside for a specific task by an anointing. In Jewish culture, kings, priests, and prophets were all anointed, and were all Messiahs in a sense. But the term had also the sense of the chosen ruler of Israel. This was not blasphemy. Many other people had claimed to be the capital-M Messiah in the time of Jesus. None of them were considered to be blasphemers.

The term Son of Man is an Aramaic idiom, according to the notes in my NRSV Harper-Collins Study Bible. In the notes for Matthew 8:20, the idiom describes a way of talking about yourself as a mere human being. In the Hebrew scriptures, one "like a human being (son of man)" was exalted by God into a position of power and judgment, and the term thus became connected to the idea of Messiah. It is one of these passages (Daniel 7:13-14) that Jesus quotes, and it's one of the few passages of the Hebrew scriptures that is actually in Aramaic (the two languages aren't the same thing, though close). The core meaning of "lowly human being" is present throughout all of this meanings, though.

Just to cover my bases here, though it doesn't appear to be in the film: Caiaphas in the Christian scriptures asks Jesus if he is the son of God, and he responds in the affirmative. This phrase would not mean the same thing at the time that it does now. John 3:16 would not be composed for another sixty years. All humans are sons and daughters of God in Jewish thought, because all participate in the Adamic image of God. Even this statement would not be blasphemy before a group of Jewish leaders, especially one careful enough to point out and disallow all the conflicting testimonies against Jesus.

UPDATE:It turns out that in this context, Caiaphas isn't asking him if he's a child of God like we all are. I was wrong. He's asking him if he claims another title that belonged to the kings descended from David.
2 Samuel 7:14 - I will be a father to him, and he shall be a son to me. (Nathan speaking for God about Solomon).

Footnote: In Israel and contemporary societies, the relation between father and son was used to express the special relationship between the dynastic deity and the king, who was regarded as the adoptive son of the national god; for David as the son of the Lord, see also Pss. 2.7; 89:26-27.

Ps. 2:7 - I will tell of the decree of the LORD: He said to me, "You are my son; today I have begotten you."

Ps. 89:26-27 - He shall cry to me, "You are my Father, my God, and the Rock of my salvation!" I will make him the firstborn, the highest of the kings of the earth.

All quotations from the Harper Collins Study Bible, NRSV.
So as you can see, the title "Son of God" isn't blasphemy, it's a title belonging to the descendant of David who is King in Israel. It's a title that belongs to the Messiah. It's not blasphemy.

So what Jesus said to the Jewish leaders he met with that night, is that he was a lowly human being created in the image of God, who was God's Messiah to lead the Jewish people. This statement was not blasphemous to the Jewish mind.

But it was palpable sedition to the Roman mind. This, then, was the crime Jesus would be executed for. Mr. Gibson portrays a judgment of blasphemy against Jesus to the detriment of his film's historical character.