anyway here are several types of distortion to avoid:

Many factors can contribute to distortion in the driver: cone behaviour,coil-end windings passing out of the main magnetic field at maximum excursion,uneven magnetic field distibution and non-linear
compliance of the cone suspension.

Other types such as doppler distortion,harmonic distortion,noise,
transient responce,clipping,intermodulation distortion.

Also what is the benefit of having a tweeter mounted inside the bass [co-axial]

Where loudspeakers are concerned, the only time I've seen people say certain types of distortion are acceptable are times when that same someone is trying to promote a pet project, probably one that produces more distortion than a competing product. Sometimes, they go so far as to say their product's distortion is euphonic, implying their speaker sounds better as a result of the distortion it makes. That's a cop-out, if you asked me. It seems to me that wherever you can reduce distortion in a loudspeaker, it is a good thing to do. That's why I like horns and drivers with shorting rings. Both are technologies that reduce distortion.