Here is the terminal log.
How do I fix it? What does it do? Is it safe or okay?
Nautilus is a graphical application so you ought to use gksudo instead :
gksudo nautilus
When you want to do graphical things with high prilivegies, gksudo and gksu are much more convinient than sudo and su.
It is an uncritical message; nautilus should run normally; for reference see this report at launchpad.