What issues can you think of that may arise from a wrong system clock setting ?
Primarily interested in potential problems affecting servers and Linux or UNIX-like systems in particular.
And how severe are these consequences, depending on how much the system time is off ? For example, 5 minutes, 30 minutes, 1 hour, 1 day.
Well for one your timestamps on all your logs will be off and out of sync with other servers making it very hard to figure out when things happened. Also, time synchronization is relied upon for some security protocols (kerberos for example).
So what I'm saying is, most things will continue working normally, some protocols or applications relying on accurate time may break, and you as the admin will generally have some headaches for it.
Configure NTP against a provider like pool.ntp.org or NIST and call it a day.
Here's just a few:
NTP is the best way to keep your time correct.
One potential source of problems I found today comes from backup or snapshots rotation scripts that rely on the fact that your clock will never go backward, or in other words, that you will never have backups named with dates and times "from the future", which may cause them to just remove those future backups / snapshots (depends on how the scripts are implemented).
Also, some versions of sudo may be vulnerable to clock rollbacks, allowing sudoers with password requirement to gain root without a password.
I'll add that two ISC DHCP servers running in failover mode will fail when the time differs by a certain threshold. They will refuse to restart after having been stopped.
Edit: depending on how it's configured, DNS can fail too because slaves won't be able to download zones from their masters and their cached zones will eventually expire.
Remote desktop and other remote access tools may stop working as they rely on time to authenticate. This can make troubleshooting very frustrating (you try to remote on to fix the problem, but can't even do that).
I had this on a machine that thought somehow thought the year was 8011 rather than 2011. SSL certificates were also expired.
My most annoying problem yet : Expiring SSL certificates. Very annoying when you can't figure out why they do not work.