Rather than skipping whole lines because they contain non-character (or mixed encoding) data -- which might be most or all of the lines -- you could just "neutralize" the non-character content, by converting it to something innocuous. Here's an example, adopting the "open" method shown above by ikegami:

use strict;
use warnings;

my $log = shift  # let's put the log file name in @ARGV
    or die "Usage: $0 name_of_input_file\n";

open(my $fh, '<:raw:perlio', $log)
   or die("Can't open input file \"$log\": $!\n");

while (<$fh>) {
    tr/\x09\x0a\x0d -~/./c;
    print;
}
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That just converts all non-visible, non-ascii bytes to "." -- which allows you to see where the non-printable stuff is, while leaving the printable ascii stuff legible, with no worries about character encoding errors.