The double quotes inside single quotes are interpreted literally and the variable expansion is not performed. You can always embed the whole sed command in double quotes (until there is no ambiguity for the shell), e.g.
Code:
sed -i "s/00\/00\/2000/${date}/g" /file.txt
Also take in mind that you can use any character as separator in the s command. This is useful when the regular expression or the replacement string contain slashes:
Code:
sed -i "s:00/00/2000:${date}:g" /file.txt