Issues with Search for Critical Point in QCD with Relativistic Heavy Ion Collisions

A systematic search for a critical point in the phase diagram of QCD matter is underway at the Relativistic Heavy Ion Collider (RHIC) and is planned at several future facilities. Its existence, if confirmed, and its location will greatly enhance our understanding of QCD. In this note we emphasize several important issues that are often not fully recognized in theoretical interpretations of experimental results relevant to the critical point search. We discuss ways in which our understanding on these issues can be improved.