I may be wrong, but I think when the scaling is non uniform e. g. (1,2,3)
then the scaled base vectors will not be orthogonal anymore.
Do you mean that the basevectors are not perpendicular anymore??
Yeah.. that can happen. It'll change the area between (0.0.0) and (1.1.1) into a parallelogram.
I think it will happen when you create a rotation matrix and scale it afterwards. But i dont think it's a problem... those are still valid basevectors. isn't it :?

Take a look here.
That page looks interesting.. i'll take a look at it when i'm home. I'm at school right now

Thank you for all the usefull info.