If I replace my syslog daemon with syslog-ng, what side effects can it have?

Glad you asked, the most common side effect is being happy with a superior syslog daemon :-)

Another common result if you compiled syslog-ng yourself is that system logfiles grow to huge sizes. This isn't syslog-ng's fault, but a side effect of syslog-ng logging to different logfiles than your old syslog daemon. Change your log rotation program's (for example: logrotate) config files to rotate the new log names/locations or change syslog-ng's config file to make it log to the same files as your old syslog daemon. If syslog-ng was installed from a package for your Linux distribution, log rotation is already configured. You should still take care for any new log destinations you create.

An alternative is to use timestamp in log file names, effectively causing log rotation to be performed automatically by syslog-ng. One still needs to take care deleting old logs. The following simple commands achieve this, which are easy to customize:

 # Find all non-Archived files that aren't from today, and archive them
# Archive Logs are deleted after 14 days
#Changes. Change -mtime +14 to the number of days to keep
# Archive old logs
/usr/bin/find /var/log/HOSTS ! -name "*.gz" -type f ! -path "*`/bin/date +%Y/%m/%d`*" -exec /usr/bin/gzip {}\;
# Delete old archives
find /var/log/HOSTS/ -daystart -mtime +14 -type f -exec rm {}\;
# Delete empty directories
find /var/log/HOSTS/ -depth -type d -empty -exec rmdir {}\;