Example:

my @data = ( "blah blah 6/20/2000 4:56 foo bar baz\n",
             "bling blang 20.6.2000 4:56 flzb gzrk\n" );

for my $string ( @data ) {
    $string =~ s{ (\d{1,2}) ([./])
                  (\d{1,2}) \2
                  (\d{4}) \s+ (\d{1,2}):(\d{2})
                }
                {
                  my @a=($2 eq ".") ? ($4,$3,$1) : ($4,$1,$3);
                  sprintf( "%s-%02d-%02d %02d:%s", @a,$5,$6 )
                }ex;

    print $string;
}
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That is, whatever string variable happens to contain one of the two types of date format, apply the lengthy "s{}{}" substitution statement to that string.

UPDATE: Forgot to mention: if you have a string with more than one date in it (e.g. "from 1/2/2000 to 3/4/2000"), just change the "ex" at the end to "exg".