Hi all, and thanks for your feedback
Jcl: I've tried both dds dxt1 and bmp for the non-transparent objects, but nothing changes.
Ventilator: these are all single-textured objects.

DaBrooz: Up until today I have been using Extra-- so materials would not help. However I just bought Commercial. After I get it installed I will post if it changes things.
UPDATE: I also tried a piece of new clean geometry with the same texture map on it, and the same problem happens with that too, so it's unlikely that it's the geometry. As I am updating to Commercial sometime today, it will be interesting to see if this phenomenon is an Extra-only problem.