server restart after timezone change

Is it required that the server should be rebooted once I change the time? I ran into trouble when I changed the datetime and did not restart crond.

Is there any other service that may have issues after time change?

A full restart is not required, but you should restart all the daemons your server actively uses. You did not tell us anything specific, but at least cron and syslog daemons should be restarted when it comes to typical system daemons.

And then you probably have some other processes needing restart, such as Apache, MySQL or Samba, whatever your server is hosting.