PERFECT information: all information available is true (no errors).
SYMMETRIC information: all decision-makers involved have exactly the same Information set
COMPLETE information: the information an agent posses includes all that is known about all aspects of the situation that we examine.
Note that when examining the information set of a single agent, neither of the above three presupposes or requires the other.
In some cases though, authors seem to use the word "Complete" in order to mean "we know everything there is to be known" about something, in some "objective" sense. Under this interpretation, it is hard (although not infeasible), to avoid identifying "complete" with "perfect", and this is why I would not suggest this approach, because a clear distinction between "complete" and "perfect" is useful. It is subtle to say (although again, not logically inconsistent) "I know everything there is to know, but some of this knowledge is wrong". It appears better to maintain a "relative" aspect to the concept of "completeness" ("all information available").