Is it bad to let my child watch tv?

Yes. The american academy of pediatrics recommends that children under 2 years of age not watch any tv at all. Children over 2 years of age should be limited to 1-2 hours of quality programming per day. Your baby will be better off with direct interaction with you and others as the first 2 years are a very critical time for brain development and tv may only serve to get in the way.
Not really. Won't hurt the eyes, but may stunt his emotional development if he watches too much.