System messages print out to the console on tty0 only, by default. If you want to use the console, switch to tty1 or above. Do this by Alt+2 (tty1), Alt+3 (tty2), etc.
When you're in Vi or another application, and syslog prints across the screen, using CTRL+L will re-draw the screen, and remove the syslog messages.
You can also disable this by editing the file /etc/syslog.conf and commenting out the following line:
*.err;kern.debug;auth.notice;mail.crit /dev/console
Simply put a # in front, save the file, and restart syslogd by doing the following as root:
# killall -1 syslogd
A much better way would probably be to redirect the output to a log file as suggested in /etc/syslog.conf:
# uncomment this to log all writes to /dev/console to /var/log/console.log #console.info /var/log/console.log