You're date variable is using / as the delimiter. As a result you aren't matching the pattern you think you are. You could just use a different delimiter for your pattern.

if ($_ = m%$dm%) {
    #stuff
}
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If you are interpolating a string it does not matter if it has characters that are the same as the delimiter. The boundaries of the regex are determined before the interpolation is done. Try this:

  perl -e '$string = "/"; print "08/14/04"=~/$string/
? "matched\n" : "no match\n"'
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