my @officialannotation = [];
my @prodigalannotation = [];
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Why are you assigning an array reference to $officialannotation[0] and $prodigalannotation[0]?

  %findgene = ( "start" => $offcordinates[1], "stop" => $offcordinates
+[0] );

 $hash_ref = \%findgene;
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Or just:

 $hash_ref = { "start" => $offcordinates[1], "stop" => $offcordinates[
+0] };
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 @officialannotation = [];
push @officialannotation, $hash_ref;
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You are removing all previous elements of @officialannotation with the assignment, and you could just write that as:

 @officialannotation = ( [], $hash_ref );
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But why do you need the array reference as the first element?    And because both %findgene and $hash_ref are at file scope the hash reference will always point to the same variable.

 for  $hash_ref ( @$officialannotation ) {
   while (my $start, $stop) =  each %$hash_ref ) {
     for $hash_ref2 ( @$prodigalannotation) {
       while (my $start1, $stop2) = each %$hash_ref2 ) {
[download]

Because the first element of @officialannotation and @prodigalannotation are ARRAY references instead of HASH references you should be getting error messages here.