The fundamental assertion of Open Theism is a fairly simple proposition - it posits that God experiences time in a fashion not unlike that of mere mortals. Unlike the more mainstream understanding of God's relationship to time - namely that God does not exist in time, nor is He constrained by it, in Open Theism, God, like man, is unaware of what the future actually is. In and of itself, that is not particularly radical or heretical - but the implications of that statement twist theologians into a lot of knots.
Prior to Creation, for example, it would have asserted that God did not know what His world would look like. It is not that he was unable to create any possibility (and that term is important for Open Theists), but rather that until he implemented any given possibility, it was not known. Asserting such a framework opens God up to the ability to form relationships, to learn, to love, and to grow as it were, precisely because he is not omnipotent.
And therein lies the crux of Piper's issue with Open Theism.
In asserting that God can grow, change, and be open to relationship, it also has the effect of making him less than omnipotent. Omnipotence itself is not a central theological point, but it is widely held, especially in evangelical circles. If God either cannot or will not be aware of his own future, then he has cut himself off from a form of power and knowledge. He must then, thus, by choice or by nature, be less than all-powerful.
Additionally, Open Theism, in opening God up to change, fundamentally must also deny the doctrine of immutability - sometimes called impassibility - or the doctrine that says, God does not change. If God can change, immutabilitists contend, then God cannot be perfect - for things that are perfect are not capable of becoming "more perfect" or "less perfect."
Beyond that, if God is constrained by time in the same way we are, his eternality is also called into question. If God can change, then there can be a time in which God is different.
Calvinists, of course, would also say that predestination becomes impossible under such a framework. While Calvinism is by no means universal, it is significant (especially amongst Evangelicals), and is a doctrine to which John Piper personally subscribes.
Finally, Open Theism calls into question the Unity of the Trinity, for if God can change over time, then he could, in theory, have different "parts" at different points in time - the heresy of partialism. If God can change, then the Members of the Trinity could, for example, disagree - a logical conundrum that would have most Trinitarians scratching their heads.
In short - it's not that Open Theism is, in and of itself, heretical - but its natural consequences lead to the overturning of many established doctrines that, if overturned, would be heretical. It's a huge leap that changes a lot of what we "know" about God, and is therefore viewed with suspicion.