Despite all of the layers and my data frame being projected using the same coordinate systems:
(Projected Coordinate System: NAD_1927_StatePlane_California_I_FIPS_0401
Geographic Coordinate System: GCS_North_American_1927)
I am still get the warning "This coordinate system has a geographic coordinate system that differs from one or more data sources in the map" when I view the Coordinate System tab in the Properties for the Data Frame. I have pressed the Transformation button and set the proper Transformation (although nothing happens when I press ok).
If all of the layers and the data frame are in the same coordinate systems, why do I continually get this error message?
It usually happens when one of the files has an incorrectly defined coordinate system and projecting it makes it worse. You will have to examine the numeric values of the extents of each layer and not rely on what you see on screen.