We have never actually bought dogs, only rescued them. That did include one purebred german shepherd who was a real sweetie, though.
The likelihood of heritable disorders is lower in mutts. It's simple genetics. With a pure breed, the gene pool is made up of individuals that are fairly closely related. Careful breeding can reduce this problem, but outcrossing to an unrelated individual is unquestionably more effective.
In some cases, the mutations or polymorphisms that cause a desired trait in a dog breed are also linked to negative effects. The cover story from the Proceedings of the National Academy of Sciences this week is a great illustration. Merle patterning in collies is desirable to some, but the same mutation that causes the coat color also causes deafness and visual problems.
However, you often get more behavioral predictability with a pure-bred dog. One reason they started the dog genome project is that there are so many behaviors predictably associated with different breeds.
We have mutts, and probably always will. There are too many wonderful dogs out there that need homes, so I can't think of a compelling reason to deal with finding a good breeder and spending all that money. I do appreciate that there are all those cool breeds out there though.