Does this do what you want? There is no need to split the sequence into an array as pos will allow you to find where in a string a match has been made. Note that [^ACGT] is a negative character class, i.e. match anything that isn't A, C, G or T. Using capturing parentheses, ( ... ), and matching globally, m{ ... }g or / ... /g will advance along the sequence looking for invalid letters.

I am opening a file that is held inside the script just to keep things tidy on my system but the code will work fine with STDIN. The code.

use 5.026;
use warnings;

open my $dnaFH, q{<}, \ <<__EOD__ or die $!;
TAAGAACAATAAGAACAAGAACAATAA
GAACAATAAGXAATAAGAAXXAACAAGAACAATAA
ACAATAAAAGAACAATAAGAA
__EOD__

while ( my $sequence = <$dnaFH> )
{
    chomp $sequence;
    my $length = length $sequence;
    say qq{Sequence: $sequence -- Length $length};
    if ( $sequence =~ m{^[ACGT]+$} )
    {
        say q{     Sequence is GOOD!};
    }
    else
    {
        my @badPosns;
        push @badPosns, pos $sequence
           while $sequence =~ m{(?x) (?= ( [^ACGT] ) )}g;
        my $nBad = scalar @badPosns;
        my $perc = sprintf q{%.2f}, $nBad / $length * 100;
        say qq{     Sequence is BAD at @badPosns};
        say qq{     $nBad bad positions, $perc\% of total};
    }
}

close $dnaFH or die $!;
[download]

The output.

Sequence: TAAGAACAATAAGAACAAGAACAATAA -- Length 27
     Sequence is GOOD!
Sequence: GAACAATAAGXAATAAGAAXXAACAAGAACAATAA -- Length 35
     Sequence is BAD at 10 19 20
     3 bad positions, 8.57% of total
Sequence: ACAATAAAAGAACAATAAGAA -- Length 21
     Sequence is GOOD!
[download]

I hope this is helpful. Please ask further if you need more help.

Update: There was a mistake in the code, I should have used a look-ahead assertion as without that pos gives the position after the match, not that of the match itself. Added extended syntax ((?x)) to make the regex clearer. My bad :-(

Update 2: I should also have corrected the output, now done.