Have the live system log displayed:
tail -f /var/log/syslog
tail -f /var/log/kern.log
Get all error messages across log files
journalctl -p err -f
or
/cat var/log/syslog |grep -iE "error|fail"
dmesg |grep -iE "error|failed"
Grab the system log from a remote server (and save on your desktop):
scp root@10.X.Y.Z://var/log/syslog ~/Desktop/syslog