The two feminine nouns are ἀκρίβεια, which could be translated "exact" or "complete." It appears only once, in Acts 22:3, which says, "I am verily a man which am a Jew, born in Tarsus, a city in Cilicia, yet brought up in this city at the feet of Gamaliel, and taught according to the perfect manner of the law of the fathers, and was zealous toward God, as ye all are this day." Adding to the confusion, it is translated as an adjective in the KJV. It is, however, a noun and refers to the accepted method of teaching.
The other feminine noun, ὁλοκληρία, could be translated "healthy" or "whole." It also only appears one time. Acts 3:16 says, "And His name through faith in His name hath made this man strong, whom ye see and know: yea, the faith which is by Him hath given him this perfect soundness in the presence of you all." Like ἀκρίβεια, ὁλοκληρία appears as an adjective in the KJV.
The verse that causes the most contraversy is Matthew 5:48, which says, "Be ye therefore perfect, even as your Father which is in heaven is perfect." Here, the text clearly says that those listening to Jesus should be like God, the Father. One must remember that Jesus is speaking to a Jewish audience that is still under the Dispensation of the Law. You and I know very well that a born again believer is not expected to be perfect, as we longingly await perfection (1 Jn. 3:2). Under the Law, the Jews were being "schooled" on the fact that they cannot be perfect, and therefore, they need a Savior (Gal. 3:21-26)!
God wants us to be perfect; that is why He sent His Son!