What can cause programmed NXT 2.0 motors to misfunction when small resistance is applied?
It turns out that the issue is a faulty/weak motor connector socket.  While randomly trying to troubleshoot, I found that if I did nothing more than press or move the cable, the motor would act bizarrely.  Initially I thought it was a bad cable, but after trying additional cables it seems that it is more likely just a poor connection at the motor. I suppose it could also be a bad motor.  The actual cause is proving very hard to pin point.

And while one motor is definitely more problematic than the others, I noticed that all of them can be made to act randomly just by pulling on the cable ends.  I am now wondering if this is common issue with the NXT and I'm considering posting another question about it.

In answer to my own question, it seems that a faulty motor connection can cause erratic behavior.