The CDC writes about adverse events:

Vaccines are developed with the highest standards of safety. However, as with any medical procedure, vaccination has some risks. Individuals react differently to vaccines, and there is no way to predict how individuals will react to a particular vaccine.

The National Childhood Vaccine Injury Act (NCVIA) requires health care providers to report adverse events (possible side effects) that occur following vaccination, so the Food and Drug Administration (FDA) and Centers for Disease Control and Prevention (CDC) established the Vaccine Adverse Events Reporting System (VAERS) in 1990. VAERS is a national passive reporting system that accepts reports from the public on adverse events associated with vaccines licensed in the United States. VAERS data are monitored to:

• • Detect new, unusual, or rare vaccine adverse events
  • Monitor increases in known adverse events
  • Identify potential patient risk factors for particular types of adverse events
  • Identify vaccine lots with increased numbers or types of reported adverse events
  • Assesses the safety of newly licensed vaccines

Interestingly, 85% of reports describe fever, local reactions, episodes of crying & mild irritability

Reportable Events (Report to VAERS)