It's perfectly safe to put stainless steel flatware in the dishwasher. Manufacturers will advise you, however, that these utensils this way may present problems if you're not careful. The hot air used in dishwasher drying cycles can increase the chance for discoloration of the pieces, as well as cause corrosion.
If you still want to put stainless steel utensils in the dishwasher, be sure to take the flatware out before the drying cycle, drying each piece by hand. Or, you can simply hand-wash your flatware. You can also attempt to dry your stainless steel at a lower temperature. If all else fails, use a stainless steel polish to wipe away discoloration or spots.