I first read the Koran ten years ago and since then have re-read many parts of it. I've also read the Classic Manual of Islamic Jurisprudence (the Umdat al-Salik); the Hadith, or sayings and deeds of Muhammad; and the Sirah, the official Islamic biography of Muhammad. I have also read around Islam, from authors both pro and anti Islam. See my library.
My conclusion: the video above is a fair and accurate summary of three key issues in Islam:
1. The doctrine of Abrogation (naskh).
2. The doctrine of Sharia, or Islamic law.
3. The doctrine of Taqiyya, or deception in the furtherance of Islam.
The end of the video gives two additional references:
The doctrine of Abrogation is particularly important to make sense of selective and contradictory quotations of the Koran.
The doctrine of Taqiyya is particularly important to understand how people -- Muslim and non-Muslim alike -- can claim that "Islam is a Religion of Peace", when all we see around us belies that contention.
On Taqiyya, I also refer you to the book "Brother Tariq: the Doublespeak of Tariq Ramadan", by Caroline Fourest. It reveals how Ramadan speaks with one voice to western audiences (smooth, comforting), and in another to Arab audiences (advance Sharia, brothers and sisters!). I've just read and enjoyed it (if that's the right word). It gets only 3 Stars on Amazon; I'd give it 4 Stars, faulting it mainly for not being tightly enough edited.