In John 5:24 when it says "does not come into judgment" is this speaking of the final judgment?
We read in John 5:24 in the KJV, "Verily, verily, I say unto you, He that heareth my word, and believeth on him that sent me, hath everlasting life, and shall not come into condemnation; but is passed from death unto life." The ASV has the word "judgment" instead of "condemnation" and I assume that this or another similar translation is the one from which the reader is posing this question.
This particular verse is not speaking of the final judgment. Verse 25 within the same context explains this for us. It says, "Verily, verily, I say unto you, The hour is coming, and now is, when the dead shall hear the voice of the Son of God: and they that hear shall live." Notice that Jesus says "the hour is coming and now is." Jesus is speaking of those who accept Him and His message during this life. Those who accept His message have the promise of eternal life, not condemnation.
The Greek word translated "judgment" here is the word "KRISIS" (from which we get our English word "crisis"). It is sometimes used in the sense of condemnation such as in Matthew 23:33 where Jesus says, "Ye serpents, ye offspring of vipers, how shall ye escape the judgment (damnation, KJV) of hell?" In our text in John 5:24, Jesus does not have in mind here the final judgment scene where both the sheep and the goats will stand before Him to be judged (Matthew 25), but rather the concept of being condemned by judicial sentence. Those who accept Him and His words will not have to worry about condemnation. Romans 8:1 says, "There is therefore now no condemnation to them that are in Christ Jesus." Jesus is not saying that some souls are going to bypass the Day of Judgment, but that those who believe Jesus' words do not have to worry about the sentence of condemnation in that Day of Judgment.