There are at least 15 examples of New Testament passages in which usages of grammatical person seem to contradict each other while textual variants of those passages do not contain such contradictions. Below are some of those passages.

Example 1: Colossians 2:13

(V₁) When you were dead in your transgressions and the uncircumcision of your flesh, He made you alive together with Him, having forgiven us all our transgressions, ⓘNASB (from Aleph & A)

(V₂) And you, being dead in your sins and the uncircumcision of your flesh, hath he quickened together with him, having forgiven you all trespasses; ⓘKJV (from Byz)

(NIV and HCSB translations agree with V₁.) Those preferring variant V₁ could not seriously argue that the writer (Paul) was excluding the Colossians from the forgiveness he spoke of. (Perhaps in some contexts, "us" could include only himself and Timothy.  See 1:1.) Still, some may wonder about the origin of the (trivial) variants. In the absence of bias toward any of the manuscripts, one may decide that "us" was changed to "you" in order to harmonize the passage. It's difficult to think of a reason why the change may have been made in the opposite direction.

Example 2: II Corinthians 8:7

(V₁) But just as you abound in everything, in faith and utterance and knowledge and in all earnestness and in the love we inspired in you, see that you abound in this gracious work also. ⓘNASB (from B)

(V₂) Therefore, as ye abound in every thing, in faith, and utterance, and knowledge, and in all diligence, and in your love to us, see that ye abound in this grace also. ⓘKJV (from Aleph & Byz)

In this passage, the apostle paul encourages the Corinthian church to emulate churches in Macedonia in regards to their generosity and earnest desire to participate in his ministry. He first commends them for their faith and knowledge. Then, according to V₂, Paul commends them for their love for him (Paul). In V₁, however, some may see a commendation to them for his own (Paul's) love for them! Certainly Paul could have been commending their love while identifying himself as the one from whom they had learned to love. Neither variant even comes close to violating Christian principles, but the question arises as to which variant (if either) is original.

Example 3: I John 1:4

(V₁) These things we write, so that our joy may be made complete. ⓘNASB (from Aleph & B)

(V₂) And these things write we unto you, that your joy may be full. ⓘKJV (from Byz)

In this beginning of the Apostle John's first epistle, he expresses his profound desire to bring his readers into fellowship with him.  He had intimate knowledge of eternal life with the Father, having personally known Jesus Christ, the Word of Life.  Variant V₂ clearly fits with John's purpose for the epistle.  V₁ could be an issue with some skeptics but it should be obvious to any modern-day disciple that "our" is not meant to exclude John's readers.  In fact V₂ could seem to be self-excluding when not considering that John had just clearly implied his own full joy in the words proceeding this verse.  Any deliberate change in the course of textual transmission could not have been some notorious attempt to distort the message.

Example 4: Galatians 4:6

(V₁) Because you are sons, God has sent forth the Spirit of His Son into our hearts. ⓘNASB (from Aleph, A, & B)

This variant makes a little more sense:

(V₂) And because ye are sons, God hath sent forth the Spirit of his Son into your hearts. ⓘKJV (from Byz)

The passage seems to be a bit illogical. It talks about the adoption of “children” (previously bound to spirits of the world) who have been adopted by God and thus received His Spirit. V₁ seems to make no sense. It could be interpreted to say “the Spirit of Christ is in my heart because someone else is a son”. There is no known additional variant of this passage. None is likely, so clearly one of these variants is original and the other is not. One was changed to the other somewhere in the transmission process. One of two scenarios is suggested: V₁ was changed into V₂, perhaps to improve sense, or V₂ was changed to V₁ for some unknown, possibly malicious, reason.

Greek Text sources cited above include:
Aleph(א) (codex Sinaiticus manuscript),
A (codex Alexandrinus manuscript),
B (codex Vaticanus manuscript),
Byz (the Byzantine manuscripts),
TR (Textus Receptus Greek text), and
GNT (Greek New Testament text).