Is dish washing liquid safe for cleaning an oven?
Considering the kinds of caustic chemicals in commercial oven cleaners (lye, KOH), I would have no fear of using dish soap.  Theoretically soap bubbles can trap flammable gas, so it's good that you rinsed thoroughly, but it's certainly less dangerous than a pool of grease.

My experience has been that vinegar and baking soda are fairly effective for cleaning ovens, you might try those next time.