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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Or you could call quotemeta() on your variable.

my $dm = quotemeta($date);
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quotemeta() will escape all non-word characters.

UPDATE: After reading hv's reply, I agree with him. SOmething didn't seem right to me as I was replying...he caught it though :)