My child was 8 weeks early and sometimes his legs and arms shake really bad. Should I be concerned?

Call your doctor. Premature babies have different health needs than full term babies. Arms and legs which shake a lot could be caused by a wide variety of conditions such as medications, imbalances in blood chemistry, seizures, and even extreme response to startling. Call your doctor today to disucss the details and arrange for an evaluation.
Maybe. Your little one could still be displaying an immature nervous system, or there may be something more going on and need to see a pediatric neurologist. Make sure your baby has had a head ultasound, but may need other imaging too.