How to check if a string contains a special character (!@#$%^&*()_+)

This is portable to Dash et al. and IMHO more elegant.

case $str in
  *['!&()'@#$%^*_+]* ) echo yup ;;
esac

Match it against a glob. You just have to escape the characters that the shell otherwise considers special:

#!/bin/bash
str='some text with @ in it'
if [[ $str == *['!'@#\$%^\&*()_+]* ]]
then
  echo "It contains one of those"
fi