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my @fileanddate;

@fileanddate = ($filename, $mtime);
$filesanddates[$filecounter] = \@fileanddate;

foreach my $filename (@filenames) {
  my $mtime=(stat ($filename))[9];
...
  # Note lexical scoping of @fileanddate
  push @filesanddates, \@fileanddate;
}

foreach my $filename (@filenames) {
  push @filesanddates, [ ( $filename, (stat ($filename))[9] ) ];
}