If we restrict the question to solid state amps, offhand I can't think of any having really poor specs that nevertheless provide top-notch sonics, but there are many renowned high quality amps whose THD and damping factor specs are not **as good** as those of many inexpensive mass market-oriented receivers and amplifiers.
Al, I think I know of an example, but its not a high-end amp, although it is highly regarded. The example is the old Sunn Concert Lead guitar amp. As a transistor amp its specs were terrible compared to the competition. But it was highly regarded because as a transistor amp it had a lot of the smoothness of tone that you otherwise only got from tubes.
The way the amp did it was to run an all-FET front end (preamp) that was zero feedback. Then the power amp was 2 single-ended gain stages that drove a transformer that did the phase splitter function for the output transistors.
As you can imagine, the primary distortion component was the 2nd harmonic. It made a lot of it! But that gave it a lusher sound that was lacking in its transistor competition (and still is), and so allowed Sunn to make a transistor amp the guitarists actually liked (most rock guitarists play tube amps because they have better sound).
IOM this is a good example of how topology influences distortion characteristics and also how that topology can thus interact with the human ear. IOW how an amp can sound better, and have terrible specs :)