Here's a slightly shorter version that I think does the same thing, using the regex engine to do all the iteration:

#!/usr/bin/perl

# Palindrome sequence http://perlmonks.org/?node_id=1117312

use strict;
use warnings;

my $contig;  # section title
my %palhash;
my $count = 0;

while(<DATA>)
  {
  $count++ < 1000 or last;
  /Contig/ and $contig = $_;

  /([CAGU]{5,20})                             # left part
    ([CAGU]{0,15})                            # middle part
    ((??{reverse($1)=~tr|CAGU|GUCA|r}))       # reverse (right) match
    (??{$palhash{$contig}{"$1*$2*$3"}++})^/x; # count found, fail
  }

for my $contig ( sort keys %palhash )
  {
  print $contig;
  for my $key ( sort keys %{ $palhash{$contig} } )
    {
    print "$key => $palhash{$contig}{$key}\n";
    }
  print "\n";
  }

__DATA__
Contig1
NAAAAGUAUAGGCUCGAGAGAGAAGUCCUGGCCUAUCGGAUUACACCACGNGUCAGAUCU
GUCACUUCAAGGAGCUUUUCAGCGUCUUUGACAAGAAUGGCNGACGGUUGCCGUCCUUCC
AGGGAGAUUGGGGCAGAAUUCGAGUCACUGCCNGUGGAUUCCUUAGUGAUCCAGAUGUCG
GAUAUAUGUCCAAUAUAGCCAAUNGUUGUUGGACAUAGCACCAUCAAUCAUCAAGAUUGC
UAUUUCGCCACCUCNAUGUAGAGUGGAAGAUCCAAAUGCGGGAAUGGAUUUCAAGGUUGG
UUAAGNAUGGGGGCAGCGGAUGAGUUAACAGUACAGCAAGCUAGGCAGCUCCAUUUNUGA
CUUGGAAUCUUCAUACGAUUCAUUUAUGGCAGCUUUGCCUAAUGUUGNGUACUUGAAAGU
AAAAUCCAAUAUUUCCAUAUUUUUGUUUAGUGCUUCAAAUCUGGUGAGAACGGAUGUUUU
AAGUUGGUAAAACAGUGUAUUCAUUUUGAAGAGUUCUUGGAUUGUUUAAAGCUCAAGAUG
CUAUUUGUGUGCUGCUGAUUUGUCGUUCUAUGAGAAAGAAUAUAUGCUUUAAUUUGGUUU
UGUAAUAUUAANUAUAUUCAUUCCCCUUGAUUGUUGUUUUGUNNNNNNNNNNNNNNNNNN
NN
Contig2
NUGUUUUUUCUUUACUCGGUGUCUCGUCGGUACUCGACGACUAAANGGGNUAUAGGAGGG
GCGCGAACGNCGAAACGGGAGUGGGUACAAAGCGUGGUCCNGGAUAGACGAGAGCGGACG
CGCCGGGUGAAGCUCGGCGCGACGCGAGGCANAGAGGGGCCCGCAGANNNNNNNNNNNNN
NNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNNN
NNNNNNNNNNAAGNCCCAGGAUGCGCAUCGCCCCAGGGGUGAAACCCCCAUCCCAAAGAA
UGCUNCUCCUNCGCGGUAGGGCAGCUNCCCGAAGCACCCGACCGCUUUNAGGCCANCCAU
AUGAUAAAGNAACGUUGUGUGGUGAAUGGGAUGAAGAUGAUUGAAGNAGAGUAGAGUUUU
GCCUCUANAUCUUGAUAUGUAUAUCUUUAAUUAUAUAANUAUAGCUCAUUAUAUUGUGCN
UUAGCAUGUAAUAUUUAAGUCUAAAAUUAANUGGACCUCAGCUCGAGGUCGNCAUUCUUU
GUUACUUUAGAUCAGAUCUGUANUUCCCUUUGUAUUGUUCAGGNUUUCCAACCAUAAAUU
AUUGGUACUAUCUUNAUUGUUAUCAUAAUUGACGUGUGUUUAAGUUCNNNNNNNNNNNNN
NNNNN
[download]

Here's the output I get:

Contig1
AAAAU*CCAAUAUUUCCAU*AUUUU => 1
AAUAU*UUCC*AUAUU => 1
AUCCA*AAUGCGGGAA*UGGAU => 1
CAAUC*AUCAA*GAUUG => 1
GAAUC*UUCAUAC*GAUUC => 1
GACGG*UUG*CCGUC => 1
GGCAG*AAUUCGAGUCA*CUGCC => 1
UAUAU*GUCCA*AUAUA => 1
UCUUG*GAUUGUUUAAAGCU*CAAGA => 1
UGGAU*UCCUUAGUG*AUCCA => 1

Contig2
ACCUC*AGCUC*GAGGU => 1
AGAUC*A*GAUCU => 1
CGCCG*GGUGAAGCU*CGGCG => 1
CGUCG*GUACU*CGACG => 1
GACCU*CAGCUCG*AGGUC => 1
GACCUC*AGCUC*GAGGUC => 1
GAUAU*GU*AUAUC => 1
GAUGC**GCAUC => 1
GGGGU*GAA*ACCCC => 1
UAUAU*CUUUAAUU*AUAUA => 1
UCGUC*GGUACUC*GACGA => 1
UCGUCG*GUACU*CGACGA => 1
[download]

By the way, there may be a problem with overlapping sequences. Your initial solution doesn't look like it allows them.