If we define perfection as "complete beyond practical or theoretical improvement" then the answer may that God is not yet perfect because humans have not always responded as God intended. There seems to be some scriptural basis for this.
For example, 2 Peter 3:9 says:
The Lord is not slow about His promise, as some count slowness, but is patient toward you, not wishing for any to perish but for all to come to repentance.
Logically, if God wishes all to come to repentance but all do not respond, then God's wish is unfulfilled. Proverbs 13:12 says "Hope deferred makes the heart sick, But desire fulfilled is a tree of life." If we apply this to the situation described in 2 Peter, then God's heart is sick, because His desire has not been fulfilled (that all come to repentance). We also get a sense of God's heart being broken elsewhere in scripture, as the prophets speak of Him as feeling like a husband whose wife has betrayed him, or as a father whose children have gone astray.
The argument for God not being perfect boils down the idea that God desires a relationship with His children and that He suffers when we do not respond to His love. Is this idea heretical, or may Christians accept it without falling into serious error?
(Note: the question does not seek arguments in favor of God's perfection/completeness, but is concerned primarily with the issue of whether or not belief in God's perfection is necessary to Christian faith.)
Addendum: I hope readers will understand the question as I have defined it (the issue of God's "completeness" as opposed to the issue of His moral perfection). I've edited the title accordingly.