Tawhano is looking more for an answer of what the Greek word in the passage is saying. There are several different meanings to the word teleios, Strongs number 5046.
Here's how they're listed
1) Brought to it's end, finished
2) Wanting nothing necessary to completeness
3) Perfect
4) That which is perfect
a. consummate human integrity and virtue
b. full grown, adult age, mature
I have to go with 4a. Consummate human integrity and virtue and here's why.
The meaing of consummate in the Websters New World dictionary is put like this:
1. Complete and perfect in every way; supreme
2. Very skillful, highly expert.
Lets look at Matthew 5:48 again shall we. Be ye perfect, even as your father which is in heaven is perfect.
We are not in heaven as the father is in heaven therefore we are unable to be like him. The father has his virtues and integrities to live by as someone living in heaven as a supreme, holy being. But we will never measure up because of this sinful flesh we live in now. We are told by Jesus that as we live as children of God we must always strive to be as the Father but we can only do so as created fallen beings.
So, be ye therefore perfect down here as your Father is perfect up there. See what I'm saying? Down here we are only going to be as perfect as our world and flesh allows us to be. God's world is that of heaven above, a place we are not in at this present time.
Yes God can and has proven to be able to live in this world and this flesh without sinning and being perfect. And although Jesus promised to send the "comforter" and that he will live in us this doesn't mean that he will take total control over us. I agree that this is what God wants but God doesn't force it. God waits for us to give in to him and his will.
What I'm suggesting, or even asking, is this. The 4a meaning of teleios can be applied to both us and God? We must strive to be consummate in our integrities and virtues as God is consummate in his integrities and virtues? Very interesting thought don't you think? I believe this could be the meaning of Matt. 5:48.
Now it's important to know that by answering Tawhano's question we are not asking ourselves what the meaning of perfect is but what the meaning of teleios is. Perfect is just an English word used by the translators that just so happends to be 1 of several possible meanings.
As I look at the english word "perfect" and find it's meaning I can't see useing this as the actual meaning of teleios in Matt. 5:48 because the useage of the word would suggest we can be flawless, without defect or omission and that would go against other scriptures saying that we all sin and must go to Jesus for forgiveness. 1 John 1:8-10, If we say that we have no sin, we deceive ourselves, and the truth is not in us. (9) If we confess our sins, he is faithful and just to forgive us our sins, and to cleanse us from all unrighteousness. (10) If we say that we have not sinned, we make him a liar, and his word is not in us. Therefore I reject the translation being that of perfect.