The following is an excerpt from Dr. Thomas Holland's Crowned With Glory, ©2000, used with permission.
Romans 8:1 - "who walk not after the flesh, but after the Spirit"
There is therefore now no condemnation to them which are in Christ Jesus, who walk not after the flesh, but after the Spirit.
The phrase "who walk not after the flesh, but after the Spirit" appears in verses one and four. Most scholars consider this a special type of scribal error called dittography, which is the repetition of a letter, syllable, word, or phrase. The thought is that a scribe accidentally copied the phrase from verse four in verse one, and that the textual error repeated itself in later manuscripts. Scribal errors do occur as is testified in the large amount of variants within the textual witnesses. However, just because a word or phrase is repeated does not mean that a scribal error has occurred.
The Greek phrase me kata sarka peripatousin alla kata penuma (who walk not after the flesh but after the Spirit) is supported by the vast majority of Greek manuscripts. Among them are 33, 88, 104, 181, 326, 330, 451, 614, 630, 1241, 1877, 1962, 1984, 1985, 2492, and 2495. These date from the eleventh to the fifteenth century. The phrase is also included in Codex K (ninth century), Codex P (ninth century), and stands in the margin of Codex Sinaiticus. This is also the reading of the majority of Greek lectionaries. Early versions that contain the phrase include some Old Latin manuscripts (such as ar and o), the Syriac Harclean version, and the Georgian version. Another textual variant that contains part of the phrase reads me kata sarka peripatousin (who walk not after the flesh). This is the reading found in Codex A, Codex D06, Codex, Y, and several minuscules (such as 81, 256, 263, 365, 629, 1319, 1573, 1852, and 2127). It is also the reading of the Latin Vulgate (fourth century  ), and the Old Syriac Peshitta. The reading in part or in whole has massive and ancient textual support.
The whole verse is cited, with the phrase in question, by Theodoret (466 AD), Ps-Oecumenius (tenth century), and Theophylact (1077 AD). We also have partial citation of the verse by Basil (379 AD). He writes:
And after he has developed more fully the idea that it is impossible for one who is in the power of sin to serve the Lord, he plainly states who it is that redeems us from such a tyrannical dominion in the words: "Unhappy man that I am, who shall deliver me from the body of this death? I give thanks to God through Jesus Christ, our Lord." Further on, he adds: "There is now, therefore, no condemnation to them that are in Christ Jesus, who walk not according to the flesh." 
When the phrase is not included it creates a possible doctrinal error. To say there is no condemnation of any kind to all who are in Christ Jesus is to overlook the whole of Scripture. We are told that it is very possible for those who are in Christ to suffer some condemnation, albeit not eternal condemnation. The Christian who walks after the flesh instead of the leading of the Spirit produces works of wood, hay and stubble (1 Corinthians 3:12). Everyone's works will be tried so as by fire. Fleshly works will be burned and spiritual works will endure. We are told, "If any man's work shall be burned, he shall suffer loss: but he himself shall be saved, yet so as by fire." (1 Corinthians 3:15). Therefore, worldly Christians face a certain amount of condemnation.
We must remember that the word condemnation not only carries the meaning of judgment, but also of disapproval.  John informs his "little children" that the heart of the believer is able to pass such condemnation or disapproval on our Christian living (1 John 3:20-21). Not only is there a judgment for believers who stand before the Judgment Seat of Christ (1 Corinthians 3:12-15; 2 Corinthians 5:9-10), but there can also be a judgment on believers that may cost them their lives if they continue in sin (Acts 5:1-10; 1 John 5:16). Biblically speaking, there is condemnation for believers who walk after the flesh and not after the Spirit. Consequently, the phrase at the end of Romans 8:1 is theologically sound.
 The Latin Vulgate was produced in the fourth century, however the earliest extant Vulgate manuscript dates from the fifth century.
 St. Basil, "Concerning Baptism," The Fathers Of The Church: Saint Basil Ascetical Works (trans. Sister M. Monica Wagner, vol. 9, New York: Fathers Of The Church, Inc., 1950), 343.
 The context of Romans 8 teaches us that faithful Christians are to walk after the Spirit and not after the flesh. The Christian is in a constant battle between the Spirit and the flesh (Galatians 5:16-18). There is no condemnation for the Believer who is following the Holy Spirit. However, there is condemnation for those who do not follow the leading of the Spirit, but seek to follow their own flesh.