Most babies are covered in a skin spot or another. What is important to take your baby to the doctor and discuss which "spots" are normal and which are not.
Don't panic! Many possibilities. Heat rash? Where are the spots? How long has your baby had them? Is your baby on any kind of antibiotics, Z-pack can do this.
No you should not be worried if your baby has red spots. One it could just be a heat rash, and that will go away pretty quick. Also, it could be a diaper rash and if you have some ointment and a warm bath that should go away within 48 hours.