To add mail subjects in Exim4 log (/var/log/exim4/mainlog), just change the /etc/exim4/exim4.conf.template file as following to add +subject to log_selector:

.ifdef MAIN_LOG_SELECTOR
log_selector = MAIN_LOG_SELECTOR +subject
.endif

Then restart Exim:

/etc/init.d/exim4 restart