Is there any significance to my son having nightmares a few times a week?

Maybe overtired?: Nightmares are more common in children who are fatigued and tend to happen in the latter half of the night (between 4-6am). Make sure your child has a consistent, relaxing bedtime routine and an early bedtime. Night terrors are different; they happen earlier in the night, and the child often is screaming, yet does not remember anything in the morning. Talk to your dr if worried.

Not necessarily: You need to distinguish between a nightmare, which means a scary dream which is remembered at least in part, and night terrors, where the child seems scared and awake but is really still asleep and has no recall of the experience. Terrors are common and usually eventually stop. Nightmares may indicate some significant stress or danger, or highlight a fear the child experiences when awake also.