The first problem with the video is how it presents the Qur'an. The Qur'an wasn't something that a person decided to write one day; It is, to us, the word of Allah ta'ala delivered to humanity through His Messenger, Muhammad (SAWS). It was revealed piecemeal over a period of more than 22 years and consists largely of commandments that are specific to a particular time and situation. As such, a few revelations became inapplicable as circumstances changed.
The "contradictions" the video mentions refer to an Islamic concept know as nasikh and mansukh, the abrogator and the abrogated. It is based on the following ayah:
Whatever message We abrogate or cause to be forgotten, We bring one better than it or one like it. Knowest thou not that Allah is Possessor of power over all things? - 2:106
There are multiple problems with claiming that all peaceful passages in the Qur'an have been abrogated. First of all, anybody making this claim takes for granted that they possess sufficient knowledge of Islam to make judgments of that importance. As non-Muslims, the makers of this video obviously do not. Secondly, there is no basis for claiming that any particular commandment has been abrogated unless there is a specific statement attributable to Muhammad (SAWS) himself that says so. Finally, it is not a consensus or even a prevalent opinion among Muslims or scholars that every call for peace in the Qur'an has been abrogated. One of the most authoritative rulings on the subject can be found in As-Suyuti's
Itqan fi 'ulum al-Qur'an. The chapter devoted to abrogation identifies 21 ayat that may be nasikh or mansukh; the rest are not. As-Suyuti was a 15th-century Egyptian expert in Islamic jurisprudence. The issue was taken up again by 18th-century South Asian scholar Shah Waliullah, who concluded that only five of As-Suyuti's verses were actually subject to abrogation. They are as follows:
2: 180, abrogated by 4: 11, 12
2:240, abrogated by 2: 234.
8:65, abrogated by 8: 62.
30:50, abrogated by 33: 52.
58: 12, abrogated by 58: 13.
In none of these instances do we find a peaceful injunction being replaced by a violent one.
If anyone can prove that each peaceful verse was abrogated by a more violent passage and back up each assertion with a specific explanation from Muhammad (SAWS), the video's claim will be correct. Otherwise, it is not.