Hi Rick,
thank you for taking the time to report this bug and helping to make Ubuntu better.

It seems you are upgrading "to" Trusty as version 2.4.31-1+nmu2ubuntu8.3 is trusty.
Is that a full precise to trusty Update with slapd formerly configured and working?

In the log I found a few issues, looking at them one by one:
#1
Preparing to unpack .../slapd_2.4.42+dfsg-2ubuntu3.1_amd64.deb ...
Unescaped left brace in regex is deprecated, passed through in regex; marked by <-- HERE in m/^(.*?)(\\)?\${ <-- HERE ([^{}]+)}(.*)$/ at /usr/share/perl5/Debconf/Question.pm line 72.

This is "just" an annoying message and fixed later on, see https://bugs.debian.org/cgi-bin/bugreport.cgi?bug=786705. So not a problem.

#2
/tmp/ubuntu-release-upgrader-15bkpjew/imported/invoke-rc.d: 1: /tmp/ubuntu-release-upgrader-15bkpjew/imported/invoke-rc.d: /sbin/runlevel: not found
 * Stopping OpenLDAP slapd
   ...done.
  Dumping to /var/backups/slapd-2.4.31-1+nmu2ubuntu8.3: 
  - directory dc=kavobv, dc=local... 58cbb2fc ldif_read_file: checksum error on "/etc/ldap/slapd.d/cn=config/olcDatabase={1}hdb.ldif"
58cbb2fc olcRootPW: value #0: <olcRootPW> can only be set when rootdn is under suffix
58cbb2fc config error processing olcDatabase={1}hdb,cn=config: <olcRootPW> can only be set when rootdn is under suffix
slapcat: bad configuration directory!
failed

That seems to have run into issues while trying to dump the DB to use it on postinst.
To do so it uses slapcat and sets a few opts.

The default is "when needed" and that is then only true if coming from before 2.4.31-1+nmu2ubuntu5 which we do in your case.

So you can trigger/test that dump manually via:
/var/lib/dpkg/info/slapd.preinst upgrade 2.4.25-1

Also enabling a set -x in that file gave me a working dump like this:
+ echo /var/backups/slapd-VERSION
+ sed -e s/VERSION/2.4.25-1/
+ dir=/var/backups/slapd-2.4.25-1
+ mkdir -p -m 700 /var/backups/slapd-2.4.25-1
+ echo /var/backups/slapd-2.4.25-1
+ dir=/var/backups/slapd-2.4.25-1
+ echo   Dumping to /var/backups/slapd-2.4.25-1: 
  Dumping to /var/backups/slapd-2.4.25-1: 
+ + read suffix
get_suffix
+ [ -f /etc/ldap/slapd.d ]
+ + cut -d: -fgrep 2
 -h olcSuffix /etc/ldap/slapd.d/cn=config/olcDatabase={-1}frontend.ldif /etc/ldap/slapd.d/cn=config/olcDatabase={0}config.ldif /etc/ldap/slapd.d/cn=config/olcDatabase={1}hdb.ldif
+ get_directory dc=lxd
+ [ -d /etc/ldap/slapd.d ]
+ get_suffix
+ [ -f /etc/ldap/slapd.d ]
+ grep -q dc=lxd
+ cut -d: -f 2
+ grep -h olcSuffix /etc/ldap/slapd.d/cn=config/olcDatabase={-1}frontend.ldif /etc/ldap/slapd.d/cn=config/olcDatabase={0}config.ldif /etc/ldap/slapd.d/cn=config/olcDatabase={1}hdb.ldif
+ cut -d: -f 2
+ grep -l olcSuffix: dc=lxd /etc/ldap/slapd.d/cn=config/olcDatabase={-1}frontend.ldif /etc/ldap/slapd.d/cn=config/olcDatabase={0}config.ldif /etc/ldap/slapd.d/cn=config/olcDatabase={1}hdb.ldif
+ sed s/^  *//g
+ grep olcDbDirectory: /etc/ldap/slapd.d/cn=config/olcDatabase={1}hdb.ldif
+ dbdir=/var/lib/ldap
+ [ -n /var/lib/ldap ]
+ [ -d /var/lib/ldap ]
+ file=/var/backups/slapd-2.4.25-1/dc=lxd.ldif
+ echo -n   - directory dc=lxd... 
  - directory dc=lxd... + [ -f /etc/ldap/slapd.d ]
+ slapcat_opts=-g -F /etc/ldap/slapd.d
+ slapcat -g -F /etc/ldap/slapd.d -b dc=lxd



I installed a slapd in Precise following [1] for the basic config and upgraded just fine.

I can before and after read the basic config the installation placed:
$ ldapsearch -Q -LLL -Y EXTERNAL -H ldapi:/// -b cn=config dn

My assumption would be that your modified confiuration is no more "dumpable" in some form.
That leads to the issues:
 checksum error on "/etc/ldap/slapd.d/cn=config/olcDatabase={1}hdb.ldif"
 olcRootPW: value #0: <olcRootPW> can only be set when rootdn is under suffix
 slapcat: bad configuration directory!

I'd ask you to either drop all config, upgrade and then set up accordingly.
Or to check your config what might cause this issue.
To do the latter you can use the "DB dumping" triggered manually as I showed above.

Since it seems likely to me that this is a local configuration problem, rather than a bug in Ubuntu, I'm marking this bug as Incomplete.

If indeed this is a local configuration problem, you can find pointers to get help for this sort of problem here: http://www.ubuntu.com/support/community

Or if you believe that this is really a bug, then you may find it helpful to read "How to report bugs effectively" http://www.chiark.greenend.org.uk/~sgtatham/bugs.html. We'd be grateful if you would then provide a more complete description of the problem, explain why you believe this is a bug in Ubuntu rather than a problem specific to your system, and then change the bug status back to New.

[1]: https://help.ubuntu.com/lts/serverguide/openldap-server.html