The best source I can give you on how flu shots don't cause people to have serious adverse responses would be the Demicheli paper cited in the references section.

It's behind the paywall, you don't happen to have a copy handy?

Also, it's interesting to look at the Demicheli abstract. It says:

Twenty five reports of studies involving 59,566 people were included. The recommended live aerosol vaccines reduced the number of cases of serologically confirmed influenza by 48% (95% confidence interval (CI) 24% to 64%), whilst recommended inactivated parenteral vaccines had a vaccine efficacy of 70% (95% CI 56% to 80%). The yearly recommended vaccines had low effectiveness against clinical influenza cases: 15%(95% CI 8% to 21%) and 25% (95% CI 13% to 35%) respectively. Overall the percentage of participants experiencing clinical influenza decreased by 6%. Use of the vaccine significantly reduced time off work but only by 0.16 days for each influenza episode (95% CI 0.04 to 0.29 days); Analysis of vaccines matching the circulating strain gave higher estimates of efficacy, whilst inclusion of all other vaccines reduced the efficacy.

An interesting question is what are the "yearly" vaccines which have such low effectiveness?