From p.20:

Jews, Christians, and Muslims worship the same God, believe in revelation, holy scriptures, heaven and hell, and have similar attitudes toward history and the role of humankind in fulfilling the divine purpose.
If I've heard or read the bolded phrase once, I've heard or read it a thousand times. Of course, it's not true. It's impossible to square a Unitarian God with a Trinitarian God. Nonetheless, "we worship the same God" is a common piece of rhetoric for those who want to bridge the faith gap. I suspect that it does more harm than good.

Brown, while apparently oblivious of this at p.20, recognized the faith gap at pp.23-24:

Indeed, the Islamic religious outlook makes it extremely difficult for Muslims to understand the Christian doctrine of the Trinity, even less to view it sympathetically. To Muslims the idea of God-in-man comes across as shirk (literally, association, thus meaning the linking of any person or thing with the ineffable God), and shirk is the gravest of sins in Islam.

Some years ago I sat in on a discussion between an eminent Egyptian ‘alim and an equally eminent Catholic priest famed for his rich, nuanced scholarly study of Islam. An exhilarating atmosphere of mutual respect and mutual understanding reigned, but then the ‘alim raised the issue of the Trinity, bringing in its wake a discussion characterized by misunderstanding and even animosity poorly papered over by scholarly politesse on both sides.
If I, as a "shirker" (say, a traditional Roman Catholic), tell a Muslim that we worship the same God, am I not blaspheming his God ?

That's the major quibble I found in Chapter 2.

Regards

Mike