SSRS 2008/SSRS 2008 R2 OLAP reports and overwriting MDX parameters

SSRS 2008 (and SSRS 2008R2) have some tremendous reporting enhancements, but unfortunately introduced a feature that caught some people by surprise. The issue is a rather intricate one, and goes as follows:

Suppose you create a report against an OLAP cube. You start by creating a report dataset, using the OLAP query designer. You drag some columns from the cube metadata into the result set area, and you also define one of the OLAP dimensions as a parameter. SSRS creates a second dataset with MDX code that retrieves member values from the dimension attribute you defined as a parameter in the primary dataset. (This allows SSRS to display the parameter values in a report dropdown).