If DNS is not configured on your server, then I'll make the assumption that sendmail is not needed at all.
Therefore, to disable the sendmail service in Solaris 10;

1) Check that SendMail is under SMF control (older Solaris 10 releases didn't have SMF, if I recall correctly)

root@blade ~# svcs -l svc:/network/smtp:sendmail
fmri         svc:/network/smtp:sendmail
name         sendmail SMTP mail transfer agent
enabled      true
state        online
next_state   none
state_time   Fri Jun 06 01:15:58 2008
logfile      /var/svc/log/network-smtp:sendmail.log
restarter    svc:/system/svc/restarter:default
contract_id  142 
dependency   require_all/refresh file://localhost/etc/mail/sendmail.cf (online)
dependency   require_all/refresh file://localhost/etc/nsswitch.conf (online)
dependency   optional_all/none svc:/system/filesystem/autofs (online)
dependency   require_all/none svc:/system/filesystem/local (online)
dependency   require_all/none svc:/network/service (online)
dependency   require_all/refresh svc:/milestone/name-services (online)
dependency   optional_all/refresh svc:/system/identity:domain (online)
dependency   optional_all/none svc:/system/system-log (online)
root@blade ~ #

2) Disable the SendMail service;

root@blade ~ # ps -ef|grep sendmail
root  2669     1   0 01:16:59 ?           0:00 /usr/lib/sendmail -bd -q15m -C /etc/mail/local.cf
smmsp  2667     1   0 01:16:59 ?           0:00 /usr/lib/sendmail -Ac -q15m
root  2950  2788   0 01:56:18 pts/1       0:00 grep sendmail
root@blade ~ # svcadm disable svc:/network/smtp:sendmail
root@blade ~ # ps -ef | grep sendmail
root@blade ~ #
However, if your interested in stopping the error without disabling SendMail, you can attempt a few things;

1) Set the hostname to the desired FQDN;
root@blade ~ # hostname
blade
root@blade ~ # hostname blade.example.com
root@blade ~ # hostname
blade.example.com
root@blade ~ #


2) Set the default domain name;
root@blade ~ # echo "example.com" > /etc/defaultdomain
root@blade ~ # cat /etc/defaultdomain
example.com
root@blade ~ #


3) Use the "domainname" command to set the default domain
root@blade ~ # domainname example.com
root@blade ~ # domainname
example.com
root@blade ~ #

Note: Just using the "domainname" command is not persistent across reboots, the /etc/defaultdomain file is read by the system at boot up, and it should contain just the desired domain ("example.com"). Doing a "domainname" after a reboot when the /etc/defaultdomain file is set will return the domain name.

4) Check the entry in /etc/hosts;
A fresh install of Solaris 10 (Update 5) left me with the following (even though I setup DNS during the OS install);
#
# Internet host table
#
::1     localhost
127.0.0.1       localhost
192.168.1.200   blade   loghost

What fixed the SendMail error for me was changing it to the following;
#
# Internet host table
#
::1     localhost
127.0.0.1       localhost
192.168.1.200   blade.example.com blade loghost