Anything more strenuous than a long hike is detrimental to totally orthodox, full-focus-on-strength-and-size Starting Strength. However, I've found that daily (or less frequent) yoga is a great supplement to powerlifting.
If you're capable of all the exercises in the program, there's no particular need for additional stretching. I've found that the exercises themselves provide a moderate degree of mobility work. I've also found that many people, particularly the un-athletic, are incapable of performing at least one of the lifts without specific stretching, mobility work, and copious warm-up.