The obvious fundamental flaw in the letter is the all too common misunderstanding (misunderstood by Christians and non-Christians alike) of the place and purpose of the law in Christianity. All of their attempts to show “unity” and similarity between Christianity and Islam are based on the law. The letter has no real mention of Gospel. Surprisingly it did refer to Jesus as messiah at least once, but there was no real acknowledgment of what “messiah” meant.
They are correct in their realization that there is One God to whom all are accountable. This is a fundamental truth. Yet it is a truth that all men know, St. Paul makes this clear in the first coulpe chapters of his epistle to the Romans. The fact that they recognize a single god does not mean they recognize the True God. The True God is the Triune God, all three parts are completely essential. This alone proves that the god of Islam is not the true God.
The most emphasized simalarity between Islam and Christianity is the letter is the common values of Love of God and Love of our neighbor. However, there can be no true unity as long as the “gods” worshipped by each group are different. There is really no hope of true peace between the two religions.
There is however potential for a temporal, worldly peace between the two religions. However, in recent History anyway (i.e. not going back to the crusades), Christians have allowed Muslims to live peacefully in their communities and predominately “Christian” countries. Muslim countries on the other hand are not at all tolerant of Christianity. Most of the responsibility for creating such a worldly peace at this point seems to fall into the hands of the muslim countries in which Christianity is not tolerated.

I have a suggestion concerning this matter. This will seem flippant but I assure you it’s not. Muslims agree to stop killing people, especially Christians, for a full year. This would demonstrate that they are sincere and actually deserve a response to their letter.

We cannot agree to love God if we cannot agree on God.
We cannot agree to love our neighbor if we cannot agree on who our neighbor is.
And we cannot agree to either, if we cannot agree on love.
The snake always appears most peaceful before it strikes. This is nothing more than a poisoned thorn offered as an olive branch.

It seems the ball is in the Christian’s court, doesn’t it, according to this open letter? Peace apparently hinges upon Christians agreeing to Muslim terms and Muslim terminology (which I don’t doubt many Christians are willing to do).
I don’t doubt the two religions can live in peace, as long as one side doesn’t physically attack the other. Simple as that. That other kind of peace these men are proposing simply can’t happen, however.
I think these Muslim spokesmen are one step away from being apologists for their own extremists, by simply ignoring them and putting the onus of peacemaking on Christians.
What would their jihadists say/do, if such a letter were addressed to them? Slap their foreheads and say they wish they’d thought of that, of our sameness?
Life, the future, human rights, let alone the triune God: show me where Islam has any intrinsic value for any of these.