Should I inspect my arrows for damage prior to each shot?

Yes.  Inspect your arrows before shooting them to determine that they are not bent or damaged.  A bent shaft or damaged nock could cause the arrow to fly in an unintended direction which could potentially cause serious injury to you or a bystander.

Inspect carbon arrow shafts for hairline fractures or cracks.  Firing a damaged carbon shaft can cause it to shatter, scattering fragments, which could seriously injure you or others.