I think it depends a lot on what kind of mutt you have, or more importantly, whether or not you know what kind of mutt you have. For example, lots of mutts have pit bull blood. If you have a pit bull mix and do not know it, you might play rough with it without treating its latent killing potential with the proper respect. Also, certain breeds tend to have certain health problems (like arthritis in labs, heat strokes in Northern breeds, etc.). If you do not know what kind of a mix your mutt is, you could be unguarded against serious maladies that could crop up at any time.
Don't hesitate to buy a mutt because it's a mutt. Just be sure you have a pretty good idea what you're getting into, first.