Not sure if this is neater or simpler, but certainly shorter - maybe you would like one of the following:

my @sections = $str =~ m/^===Comments===\n(.*?)\n=.*?=$/gms;

print Dumper(\@sections);


print "\n\nOR\n\n";


my %sections = reverse( $str =~ m/^===Comments===\n(.*?)\n=(.*?)=$/gms
+ );

print Dumper(\%sections);

print "\n\nOR\n\n";

while($str =~ m/^===Comments===\n(.*?)\n=(.*?)=$/gms) {
    print " $2 : $1\n";
}
[download]

Which produces:

$VAR1 = [
          '
User comments are added here. A user may write whatever they may wish.
',
          '
Comments are related to the microarray data here.
',
          '
Comments related to the pathway information here.
'
        ];


OR

$VAR1 = {
          'Microarray Data' => '
User comments are added here. A user may write whatever they may wish.
',
          'Pathway Information' => '
Comments are related to the microarray data here.
',
          'Aditional Info' => '
Comments related to the pathway information here.
'
        };


OR

 Microarray Data : 
User comments are added here. A user may write whatever they may wish.

 Pathway Information : 
Comments are related to the microarray data here.

 Aditional Info : 
Comments related to the pathway information here.
[download]

update: but I see the last two are wrong, now that I've posted it.

my %x = map {
    /^=([^\n]*)=\n.*\n===Comments===\n(.*)$/s ? ( $1 => $2 ) : ()
} split(/(?=^=[^=])/m,$str);

print Dumper(\%x);
[download]

gives

$VAR1 = {
          'Microarray Data' => '
Comments are related to the microarray data here.

',
          'Pathway Information' => '
Comments related to the pathway information here.

',
          'Literature' => '
User comments are added here. A user may write whatever they may wish.

'
        };
[download]

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