The first major thing that leapt out at me was when Omaar discusses Muhammad's marriage to nine-year-old Aisha, and makes out that her age can reasonably be disputed depending on who you ask, and that she could just as easily have been 16.
It's certainly true that some people will tell you that Aisha was a lot older than nine, but this claim flies completely in the face of the Islamic textual evidence. Five of the six Sahih Sittah (the most revered hadith collections) contain explicit testimonies that Aisha was nine at the time Muhammad consummated his marriage with her. Below is but one example from each collection, although there are many similar traditions to choose from:
Khadija died three years before the Prophet departed to Medina. He stayed there for two years or so and then he married 'Aisha when she was a girl of six years of age, and he consumed that marriage when she was nine years old. (Bukhari v.5, b.58, no.236)
'A'isha (Allah be pleased with her) reported that Allah's Apostle (may peace be upon him) married her when she was seven years old, and he was taken to his house as a bride when she was nine, and her dolls were with her; and when he (the Holy Prophet) died she was eighteen years old. (Muslim b.8, no.3311)
Aisha said: The Apostle of Allah (may peace be upon him) married me when I was seven years old. The narrator Sulaiman said: Or six years. He had intercourse with me when I was nine years old. (Abu Dawud no.2116)
When Hadrat Aisha passed nine years of marriage life, the Holy Prophet Muhammad (peace and blessings of Allah be upon him) fell in mortal sickness… ‘A’isha was eighteen years of age at the time when the Holy Prophet (peace and blessings of Allah be upon him) passed away and she remained a widow for forty-eight years till she died at the age of sixty-seven. (Nasai)
1877. Abdullah (Allah be pleased with him) is reported to have said, "The Holy Prophet (peace and blessings of Allah be upon him) married ‘A’isha while she was a seven years [sic] old girl and took him [sic] to his house as a bride when she was nine years old and he parted with her (after his demise) when she was eighteen years old." (Ibn Majah)
Other important Islamic historical sources, including the biographies of Ibn Hisham, Tabari and Ibn Kathir also state explicitly that Aisha was nine. There is no evidence anywhere that she was older, except for circumstantial evidence which largely involves focusing on apparent timeline discrepancies, while ignoring every single authoritative text that says in black and white that she was nine. Omaar has thus created a "dispute" where there is none.
He does this again when it comes to Muhammad's multiple marriages. He allows Karen Armstrong to claim - again with no evidence at all - that the Prophet of Islam's polygamous marriages were not borne of lust, but were purely marriages of political convenience. This once again ignores what the most respected Muslim sources on Muhammad's life actually say. Muhammad resolved to marry his adopted son's wife, for example (who was known for being very beautiful), after accidentally walking in on her in a state of undress, which in the words of the famous Muslim historian Tabari "excited the admiration of the Messenger of God". (The History of al-Tabari, v.8, p.2)
Another wife, Safiyya bint Huyayy, was taken by Muhammad as a war captive after his attack on the Jewish oasis of Khaybar, and chosen specifically for her beauty:
We arrived at Khaibar, and when Allah helped His Apostle to open the fort, the beauty of Safiya bint Huyai bin Akhtaq whose husband had been killed while she was a bride, was mentioned to Allah's Apostle. The Prophet selected her for himself, and set out with her, and when we reached a place called Sidd-as-Sahba,' Safiya became clean from her menses then Allah's Apostle married her. (Bukhari v.5, b.59, no.522)
What any of this had to do with political or tribal calculations is anyone's guess.
One of the most egregious falsehoods in the entire series comes when Omaar describes Muhammad's takeover of Mecca as a wonderfully peaceful event, during which he declared a general amnesty and forgave every single one of his enemies. As the useful website Religion of Peace put it so superbly: "If the fact that an entire city wasn’t put to the sword after being conquered by a man against whom it did not want to fight is proof of forgiveness, then we would have to say that the bar is being set quite low."
In any case, Muhammad actually ordered the assassination of a number of his enemies upon taking control of Mecca, although not all the murders were eventually carried out. The unfortunate souls who were indeed murdered included Abdullah Khatal, an apostate, and one of his slave girls, as well as the Jews Abu Afak and Asma bint Marwan, both of whom were killed (as was Abdullah's slave girl) for the crime of "insulting" Muhammad by writing satirical verses.
Omaar also omits all mention of the way that, following his conquest of Mecca, Muhammad subdued the rest of Arabia by imposing Islam upon all the remaining tribes by force. One tribe in Yemen was told, "Break them (i.e. the arrows) and testify that None has the right to be worshipped except Allah, or else I will chop off your neck." (Bukhari v.5, b.59, no.643) Muhammad sent his most fearsome warrior, Khalid bin Walid, to the Banu Harith tribe, and "ordered him to invite them to Islam for three days before he fought them. If they were to respond and submit, he was to teach them the Book of Allah, the Sunnah of His Prophet, and the requirements of Islam. If they should decline, then he was to fight them." (Tabari v.9, p82)
You get the picture. Overall, non-Muslims have very little to learn from this series of documentaries, except that Muhammad was always and everywhere a victim, and managed to convince the whole of Arabia to convert to Islam simply by being so wonderful. I don't know how many people will buy it, but for those who felt unsure what to believe during and after watching the three episodes, I hope my analyses of some of their contents have been useful and instructive.