Yes, vegetables really should be washed to remove unseen pesticides, bacteria, and mold. Rinsing with water does a fair job, but to be safe, try the following:
Combine a cup each of water and white distilled vinegar in a spray bottle. Add two tablespoons of baking soda and one tablespoon of lemon juice. Use by first shaking, then spraying generously on your raw vegetables. Let sit for five minutes, rinse with water, then proceed with your cooking plans.