• Including what the error message is will get better replies.
• perl -wc foo can be enlightening.
• `@annotation' and `@annoation' are two different things
• All through get_dna you're treating (or trying to treat at least) $seq as a scalar reference, but you don't pass a scalar reference when you call it
• m{^//n} is easier to read than something with all the backwhacking of `/'s.
• In your second elsif you set $seq when you probably meant to set $in_sequence

You probably want something like this but as you don't describe what this code is supposed to do (and it is somewhat incomprehensible) I am kinda guessing

#!/usr/local/bin/perl -w

use strict;

print "Please type in the name of a file\n";
my $file = <STDIN>;
chomp $file;

my ($annotation, $seq) = get_dna ($file);

# convert $annotation array reference to a real array
my @annotation = @$annotation;

print "Annotation:\n\n", @annotation, "\n\n\n";
print "Sequence:\n\n", $seq, "\n";

sub get_dna {
    my ($file) = @_;
    my @annotation = ();
    my $seq = '';
    my $in_sequence = 0;
    open FILE, $file or die "Can't open $file, Perl says $!\n";
    while ( my $line = <FILE> )    {
      last if $line =~ m|^//\n|; # stop if line has just // on it
        $in_sequence = 1 if $line =~ m/^ORIGIN/;
        if ($in_sequence) {
            $seq .= $line;
        } else {
            push @annotation, $line;
        }
    }
    close FILE;
    # remove all spaces and digits from $seq. add \n to remove newline
+s
    $seq =~ s/[\s0-9]//g;
    # return @annotation array as a scalar reference and scalar $seq
  return \@annotation, $seq;
}
[download]

cheers

tachyon

s&&rsenoyhcatreve&&&s&n.+t&"$'$`$\"$\&"&ee&&y&srve&&d&&print

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

use Bio::SeqIO;

my $seqobj;

print "please type in the name of a file\n";
my $file = <STDIN>;

my $seqio  = Bio::SeqIO->new (-format => 'GenBank',
                              -file =>   $file);
while ($seqobj = $seqio->next_seq())
{
  printf "Sequence: %s\n",$seqobj->seq;

  # I'm not sure what you need other than the
  # sequence - here's some examples:
  printf "Display ID:  %s\n",$seqobj->display_id;
  printf "Description: %s\n",$seqobj->desc;
  printf "Division:    %s\n",$seqobj->division;
  printf "Accession:   %s\n",$seqobj->accession;
}
[download]