In your original code, the value of $_ gets clobbered after the recursive call to read_cal. The work around is to save the input line into a temporary variable, instead of relying on the Perl built-in $_ variable which can get modifed due to side effects somewhere else in the script.

I have modified your script and I believe the following will work without problem -

#!/usr/local/perl/bin/perl -w
use strict;

my %hash;
my $cal = shift;

read_cal($cal, 0);
foreach my $file (@ARGV) {
    read_cal($file, 1);
}

foreach my $key (sort keys %hash) {
    print "$key\n" if $hash{$key} == 1;
}

sub read_cal {
    my ($cal, $mode) = @_;

    print "---------------$cal-----------------\n";

    my $fh;
    open($fh, $cal) or die;
    while(my $line = <$fh>) {
        chomp($line);
        next if $line =~ /^\s*$/;
        next if $line =~ /^#/;
        $line =~ s/\s//g;
        # print "before $cal, |$line|\n";
        read_cal(substr($line,1), $mode) if $line =~ /^I/;
        print "|$line|\n";
        my $schedule = (split ':', $line)[-1];
        if (!$mode || exists $hash{$schedule}) {
            $hash{$schedule}++;
        };
    }
}
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