#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

my $dict = '/var/lib/dict/words';  # YMMV

sub each_char_has_different_freq {
    my ($r, $f) = @_;
    keys %$r == keys %$f
}

sub frequencies_form_a_sequence {
    my ($r) = @_;
    keys %$r == grep $r->{$_}, 1 .. keys %$r
}

my @linenlessnesses;
open my $IN, '<', $dict or die $!;
while (<$IN>) {
    chomp;
    next if /\W/;

    my %freq;
    $freq{$_}++ for split //;

    my %r = reverse %freq;
    push @linenlessnesses, $_
        if each_char_has_different_freq(\%r, \%freq)
        && frequencies_form_a_sequence(\%r);
}
say for sort { length $a <=> length $b } @linenlessnesses;
[download]

Interesting output (the longest words) on my machine:

deadheaded
evennesses
keennesses
peppertree
rememberer
restresses
sanenesses
sereneness
sleeveless
sussararas
susurruses
[download]

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]