Comment 3 for bug 1501884

Brad, what's to diagnose? I've done all the diagnosis for you already. Anyway, here's the relevant snippet from the dpkg log with the problematic line highlighted:

(Reading database ... 149768 files and directories currently installed.)
Removing linux-headers-3.13.0-63-generic (3.13.0-63.103) ...
Removing linux-headers-3.13.0-63 (3.13.0-63.103) ...
Removing linux-image-extra-3.13.0-63-generic (3.13.0-63.103) ...
run-parts: executing /etc/kernel/postinst.d/apt-auto-removal 3.13.0-63-generic /boot/vmlinuz-3.13.0-63-generic
                                                                 ^^^^^
run-parts: executing /etc/kernel/postinst.d/initramfs-tools 3.13.0-63-generic /boot/vmlinuz-3.13.0-63-generic
update-initramfs: Generating /boot/initrd.img-3.13.0-63-generic
run-parts: executing /etc/kernel/postinst.d/update-notifier 3.13.0-63-generic /boot/vmlinuz-3.13.0-63-generic
run-parts: executing /etc/kernel/postinst.d/zz-update-grub 3.13.0-63-generic /boot/vmlinuz-3.13.0-63-generic
Generating grub configuration file ...
Found linux image: /boot/vmlinuz-3.13.0-65-generic
Found initrd image: /boot/initrd.img-3.13.0-65-generic
Found linux image: /boot/vmlinuz-3.13.0-63-generic
Found initrd image: /boot/initrd.img-3.13.0-63-generic
Found memtest86+ image: /boot/memtest86+.elf
Found memtest86+ image: /boot/memtest86+.bin
done

Here is the content of /var/lib/dpkg/info/linux-image-extra-3.13.0-65-generic.postrm, again with highlight:
#!/bin/sh
set -e

case "$0::$1" in
*.postinst::configure|*.postrm::remove)
 depmod -a -F /boot/System.map-3.13.0-65-generic 3.13.0-65-generic || true
 for dir in "/etc/kernel/postinst.d" "/etc/kernel/postinst.d/3.13.0-65-generic"
                                                   ^^^^^^^ ^^^^^^
 do
  if [ -d "$dir" ]; then
   run-parts --verbose --exit-on-error --arg="3.13.0-65-generic" --arg="/boot/vmlinuz-3.13.0-65-generic" "$dir"
  fi
 done
 ;;
esac

All those postinst.d should be postrm.d