Try this on for size... Probably still not the way I would approach the problem, but at least it's a bit more elegant...

my $srcdir ='/var/local/some_dir';
my $mtime = 1;
my $destdir = '/backup/some_dir';

# Yours doesn't tell you which directory didn't exist...
die "$srcdir does not exist" unless -d $srcdir;
die "$destdir does not exist" unless -d $destdir;

print "Beginning backup...\n";

# Error checking on chdir is important too, the directory
# might exist, but not be readable by you
chdir $srcdir or die "Can't change to $srcdir: $!";

# Once your program gets bigger than a couple of lines,
# you really want to know which directories or files
# couldn't be opened
opendir ( INDIR, $srcdir ) or die "Can't open $srcdir: $!";

# if this is a big directory, slurping all the files into
# memory can be quite a waste of memory...
while ( my $file = readdir( INDIR ) ) {
    next if -d $file; # -d will be true for . and .. too
    if ( -M $file > $mtime ) {
        print "$file : Older than one day.\n";
        next;
    }
    # tar is for combining multiple things into one,
    # gzip is for compressing, since you are only doing
    # one file at a time, the tar is just wasted effort
    system( "gzip -c $file > $destdir/$file.gz" );
    if ( $? != 0 ) { die "Gzip failed" }
    print "$file archived in $destdir\n";
}
[download]

This is probably how I would actually approach the problem... Although this approach may not meet some requirements that couldn't really be inferred from your code...

use Path::Class qw( dir );
my $srcdir = dir( '/var/local/some_dir' );
my $destdir = dir( '/backup/some_dir' );

$destdir->mkpath unless -d $destdir;

die "$srcdir does not exist" unless -d $srcdir;
die "$destdir does not exist" unless -d $destdir;

print "Beginning backup...\n";

while ( my $file = $srcdir->next ) {
    next if $file->is_dir;
    my $target = $destdir->file( $file->basename.".gz" );
    if ( $file->stat->mtime <= $target->stat->mtime ) {
        print "backup is more recent than original\n";
        next;
    }
    system( "gzip -c $file > $target" );
    if ( $? != 0 ) { die "Gzip failed" }
    print "$file archived in $destdir\n";
}
[download]

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