The Define Projection tool functionality is not consistent from ArcGIS Desktop 9.1 to 9.2. Furthermore, in 9.2 it allows the reprojection of shapefiles that have an existing defined projection.
Use the Projection Tool (ArcToolbox > Data Management Tools > Projections and Transformations > Feature > Projection) to reproject a coordinate system for a file that has a defined projection. 09/05/07 JL- This test also produced drawing errors. Bug still exists.