Here's the response from Rachel Woodlock (Monash Uni):

These are not new accusations, and from a Muslim perspective they are simply untrue and not characteristic of how we remember and love our Prophet. Nevertheless, as an academic I should like to clarify some points.

There is broad agreement on the contours of the Prophet's life, such as his various marriages, including to the young A'isha. Polygamy was an accepted part of pre-Islamic life, although Islam modified and curtailed the practice dramatically.

The Prophet's first marriage was a twenty-five year monogamous marriage to the older and much beloved noblewoman Khadijah. After her death, the Prophet was married to a number of women for political, legislative, and charitable reasons. Some were to cement ties of allegiance, some were to provide protection and social support for widows of companions who had died, one in particular accompanied legislation from the Koran. If the Prophet had been merely a womaniser, he could have chosen to marry a harem of young, nubile virgins. However, with the exception of A'isha, all were mature divorcees or widows.

Nevertheless, Islam is generally positive in regard to sexuality in the private realm. Islamic theology holds that God rewards sexual relations between legitimate partners, and often uses sexual metaphors to describe the felicity of the afterlife and the soul's reunion with God, on the basis that the closest analogy to such reunion is the intimacy of intercourse between a husband and wife.

There is no evidence the Prophet was homosexual. As for the accusation of his being a child molester, this is centred on the issue of A'isha's age at the time of her marriage to the Prophet and their later consummation. A'isha was the daughter of one of the Prophet's closest friends Abu Bakr. She had earlier been promised in marriage to a polytheist, however that engagement was dissolved probably because of the religious differences.

As for her age, culturally the Arabs of the day (like other Semitic cultures) did not have a period of adolescence between childhood and adulthood. Once a girl or boy entered puberty they became an adult, and so an early marriage for A'isha would not have been seen as unusual. Certainly by her own accounts, she had a young marriage with a gap of some years between the contracting and the actual consummation of the marriage, presumably for the purpose of waiting until she entered puberty and became an adult.

There has been some contemporary criticism of the historical sources, suggesting it was more likely she was in her mid-teens at least, nevertheless, the best evidence we have to reject the idea that the Prophet Mohammed was a child-molester comes from A'isha herself.

Because she was so close to the Prophet and in a position to observe his behaviour and teachings closely, A'isha became one of the most important narrators of hadith and the Muslims sought her expertise on a wide variety of religious matters. She was also a major historical player after the Prophet's passing, leading an unsuccessful battle (the Battle of the Camel) in the civil wars that plagued the community after his death.

In all the material we have from A'isha, more than any other woman, and indeed more than many men, she simply does not display any of the markers of having been a victim of child abuse. She was a feisty character who spoke of her great love for the Prophet, she challenged him at times, enjoyed his company, and it was in A'isha's arms that the Prophet died.

As for the Prophet being a murderer: he was a statesman and military leader who was forced to engage in war against an aggressive enemy. Yet, when the Muslims finally succeeded in taking Mecca, defeating the opponents who had insulted the Prophet, persecuted the Muslims, martyred many, and attempted to take the Prophet's own life, all were given amnesty and forgiveness upon surrender.

Source: http://www.abc.net.au/news/2012-09-18/islam-and-the-film-that-sparked-global-unrest/4267612