$date=~/(\d{1})\/(\d{2})\/(\d{4})/ This matches 1 digit for month (= "0") and not 2. Better would be:

$date=~/(\d\d?)\/(\d\d?)\/(\d{4})/
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or, if you want curly braces:

$date=~/(\d{1,2})\/(\d{1,2})\/(\d{4})/
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or, if you like to check more:

$date=~/(0?[1-9]|1[0-2])\/(0?[0-9]|[12]\d|3[01])\/(\d{4})/
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