I'm not sure I understand your question. The most common way to print a message and exit is with die:

$date1 =~ /(\d\d)(\d\d)(\d\d)/
  or die "Invalid date format";
$time1 =~ /(\d\d):(\d\d)/
  or die "Invalid time format";
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Or are you talking about catching the error from gmtime? You're doing that properly, and I don't believe there's a better way to do it. When I have code like this, I will often wrap the entire thing in an eval, like this:

eval {
    my $ref = shift;
    my $date1 = shift @$ref;
    my $time1 = shift @$ref;
    die unless $date1 =~ /(\d\d)(\d\d)(\d\d)/;
    my @date2 = ($1,$2,$3);
    die unless $time1 =~ /(\d\d):(\d\d)/;
    my @time2 = ($1,$2);
    my $t;
    $t = timegm(0,$time2[1],$time2[0],$date2[1],$date2[0]-1,$dat
+e2[2]+100)};
};
print "-1\n" and exit if $@;
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It consolidates the error handling better.