The idea of having a peaceful, multi faith center where people of all different religions can meet and truly communicate like people of the 21st century is something we all need. It is Multi faith, not just Islamic, which many people are against due to its location near Ground Zero. It is not a Mosque, or a Church, or a Synagogue. It is a place where all can meet.
Doomed to fail. Unlike the idea of the United Nations, religion is far less likely to mingle peacefully. Look at Jerusalem where there has been a long violent history in the past.
During its long history, Jerusalem has been destroyed at least twice, besieged 23 times, attacked 52 times, and captured and recaptured 44 times.
Today, it is shared by Jewish, Muslim, and Christians but this peace is only surface deep. It has been broken up into separate parts for each religion with armed troops patrolling to make sure peace is kept. The only other reasons why they don't constantly fight is because it would probably ruin their own religious sites in the process and could mean the end of their welcome to what they feel is one of if not the most important holy sites. For the most part, even in the areas where they do cross paths, they still rarely speak to each other much less meet.
The first major obstacle would be the "who's in charge" business. Obviously, none of them would accept the rule of a different religion. On the odd chance that they may talk with each other, the inevitable discussion would lead to an argument that would lead to much worse. Seeing that there religion makes no claim to the buildings spiritual meaning they would not value it or care if it got damaged or destroyed. In fact, a radical version of one of those religions would probably consider this building as evil and worthy of destruction like the towers in New York.