Inspect the rooms at least once a week if you choose to close them off. All is not perfect when using space heaters. A properly designed and installed central system will keep the whole house near the same temperature. As you move about the house, cool rooms seem cold, and warm rooms feel hot. You then start adjusting thermostats, which can reduce your savings.
Space heaters present more opportunities for something to go terribly wrong than with central heat.
Space heaters allow you to place flammables close enough to the heating elements to ignite them. While some added indoor humidity is often welcome in the winter, too much moisture can cause uninsulated walls and windows to sweat. The water can make your home more desirable to wood-eating insects and fungi. Carbon dioxide will not sustain life. CO can have much more serious consequences.