What is the "violence" (Gen 6:11) that prompted God to bring on the Great Flood during the time of Noah?

Violence

The word translated as violence here is חָמָס. It can also mean corruption, cruelty, etc. From the previous verses (6:5-6) we get the sense that violence is one of many issues that motivated God's grief over humankinds sins.

When the Lord saw that man’s wickedness was widespread on the earth and that every scheme his mind thought of was nothing but evil all the time, the Lord regretted that He had made man on the earth, and He was grieved in His heart.

Vegetarianism

The "green agenda" issue may be played up in the film, but it does find confirmation in the text. Prior to the Flood, the film suggest that Noah followed the guidelines set by God for Adam and Eve in Gen 1:29:

Look, I have given you every seed-bearing plant on the surface of the entire earth and every tree whose fruit contains seed. This food will be for you...

After the Flood, God permitted Noah and his descendants to eat meat:

Be fruitful and multiply and fill the earth. The fear and terror of you will be in every living creature on the earth, every bird of the sky, every creature that crawls on the ground, and all the fish of the sea. They are placed under your authority. Every living creature will be food for you; as I gave the green plants, I have given you everything. (Gen. 9:1-3)

The Book of Enoch

The film draws a lot on The Book of Enoch, which is not part of the Jewish or Christian canon (except for Ethiopian churches). This book describes the story of the Nephilim of Gen. 6 in great detail and was apparently the source for much of the film's plot. Enoch was well known in the time of Jesus. In fact NT's Letter of Jude quotes Enoch as a prophet and speaks of the book's content, referring to:

...the angels who did not keep their own position but deserted their proper dwelling. In the same way, Sodom and Gomorrah and the cities around them committed sexual immorality and practiced perversions, just as angels did, and serve as an example by undergoing the punishment of eternal fire. (1:6-7)

If one knows only the Genesis account, the film certainly takes far too many liberties. However, Genesis does support the idea that Noah's family did not eat meat until after the Flood. Beyond Genesis, reading the Book of Enoch will provide an appreciation for the filmmakers' attempt to portray the story of the Nephilim and Noah, even if the movie did not adhere closely to the Bible.

Further Reading: The Book of the Watchers first part of the Book of Enoch.

You ask, "To what degree does the film's portrait of "violence" find confirmation in the text of Genesis? [and] To what degree are the movie makers distorting Genesis in order to falsely portray God and Noah as advocates of a "green agenda"? The first distortion worth mentioning is about something that is missing throughout the entire film.

Strangely, in this epic story nobody mentions "God" - not even Noah. Could there be a hidden agenda behind this film - write God out of the script?

Christians are not surprised that the account of Noah and the flood has been portrayed this way. We expect the Bible to be misrepresented and that every attempt will be made to shut God out. Noah only gets a hint from the Creator of the coming flood. Just as Monty Python’s Life of Brian pastiched the life of Christ, this Noah is falsely portrayed as a killer who is out to put a sword through anyone who happens to think too much.

Appallingly, the film has Noah misunderstanding things, thinking the Creator wants him to destroy all humanity, plus his own family. The idea of God regenerating an utterly evil and wicked society does not figure. But Noah is supposed to be guided by hallucinations induced by herbs, and to be in a surreal 'world'.

Equally unwarranted, unbiblical points are randomly inserted. No wives for Ham and Japheth; Methuselah is an esoteric medicine man; snakeskin being passed down through Noah’s family is supposedly important. As for the 'violence' part of the question, the Bible speaks clearly and unambiguously:

"The earth also was corrupt before God, and the earth was filled with violence. And God looked upon the earth, and, behold, it was corrupt; for all flesh had corrupted his way upon the earth." Genesis 6:11-13 A.V.

Noah, however, was neither corrupt nor violent due to his great faith in God, and so "Noah found grace [favour] in the eyes of the Lord... Noah walked with God" (vss. 8 & 9) - this in contrast with the revulsion God felt at the rest of corrupted, violent humanity.

The suspicion that this film is not based on the Bible but upon Kabbalah – Jewish Gnosticism – seems warranted. The film seems designed to promote humanism, environmentalism, Gnosticism and vegetarianism, which will delight some people, no doubt, but avoids the real issues the book of Genesis shows as of vital importance – God will judge unrepentant evil-doers, but he shows grace to those who reverence Him. And Jesus spoke of the time before he returns to Earth as being like the days of Noah, particularly with people taking no note of God before destruction falls upon them. Mat. 24:36-44