Ok, problem found. The geometry service I was using was on sampleserver1 running ArcGIS 9.31 and the lengthUnit parameter is not present.
I guess my issue now is that a user of mine may very well configure an ArcGIS 9.31 geometry service to be used in my viewer. I must detect this, and if so I will need to do all the unit conversion myself, based on what measurement units are being returned.
In this case, I'll need to obtain the measurement unit used for a particular spatial reference. Hopefully ArcGIS provides an easy way to do this.
Thanks for the help!