Thanks for the feedback so for, a first update based on the suggestions would be:

#!/usr/bin/perl

use strict;
use warnings;
use diagnostics;

use File::Find;
use Date::Format;
use Date::Parse;

sub process {
    if (-f $_ && /\.html$/) {
        my $fn = $_;

        open(F, "<:utf8", $fn) or die("Cannot open ${File::Find::name}
+: $!");

        my ($in_text, $in_subject) = undef;
        my ($text, $subject, $time);
        while (<F>) {
            chomp;

            if ($_ =~ /\w+, (\w+ \d\d, \d{4})/) {
                $time = str2time($1);
            } elsif (/<h3 class="post-title">/) { # Subject
                $in_subject = 1;
            } elsif ($in_subject && $_ !~ m%</h3>%) {
                $subject = $_ if /\w/;
            } elsif ($in_subject && $_ =~ m%</h3>%) {
                $in_subject = undef;
                $text = "$subject\n";
            } elsif (/<div class="post-body">/) { # Text
                $in_text = 1;
            } elsif ($in_text && $_ !~ m%</div>%) {
                $text .= $_ . "\n";
            } elsif ($in_text && $_ =~ m%</div>%) {
                last;
            }
        }

        die "Invalid fileformat: $text $time." unless ($text && $time)
+;

        $text =~ s/(\r|<p>|<\/p>|^\s*)//gm;
        $fn =~ s/html$/txt/;

        open(OUT, ">:encoding(iso-8859-15)", "/home/hynek/old-blog/new
+/$fn") or die "Cannot open for write: $!.";
        print OUT $text;
        close(OUT);
        utime $time, $time, ("/home/hynek/old-blog/new/$fn");
    }
}

find(\&process, ("tmp"));
[download]

Now I'm going to read it flatly and try to utilitize the ".."-operator...let's see how it further shortens the script (comments on this code are still welcome though).