Actually, regarding my problem, it doesn't make a difference to localize $|.

My server now looks like this, but has the same hang

#!/usr/bin/perl -w

use strict;

    local $| = 1;

    print "Content-Encoding: iso-8859-1\015\012",
                "Content-Type: text/plain\015\012",
                "\015\012";

    warn "DEBUG: the content length is $ENV{CONTENT_LENGTH}\n";

    my $returncode = read(STDIN, my $post_content, $ENV{CONTENT_LENGTH
+});

    warn "DEBUG: the read returncode was $returncode\n";
    warn "DEBUG: Finished.";
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Stas Bekman has summed up why one would use $| = 1 under mod_perl quite well in mod_perl: Performance Tuning.