First though, thank you for the kudos, how great or little they may be deserved. I must point out that with my refutation, your title "3 Good Examples of Bible Errancy" is somewhat ironic. With that said, let us move on:
The last words of Christ, as found in the Gospels of Luke and John, upon just a cursory reading, would seem to be contradictory. However, the truth comes only after careful study, as commanded in Scripture (II Tim. 2:15). To arrive at the truth, we must first start with the origin and authors of the Gospels.
Matthew was one of the twelve apostles, and the first to record the message of Jesus Christ, as was being preached and told in the churches. His account of the crucifixion was most likely first hand, and yet it does not mention the exact last words spoken by Christ. Matthew simply says Christ cried out in a loud voice.
The Gospel of Mark was not written by an apostle, nor was the account of the crucifixion first hand. Mark was the nephew of Barnabas, and after leaving his uncle and Paul, returned to Jerusalem, where he served with Peter. Mark's Gospel is most likely a record of the message he heard Peter preaching day in and day out. Mark also does not record the exact last words of Christ, but merely says he cried out in a loud voice.
Luke was a companion of the Apostle Paul, and his Gospel is a record of the message preached by Paul. Paul never says he was an eyewitness of the crucifixion, but it is possible he was a member of the great multitude, especially since he was a Pharisee. Regardless, Paul received his message through special revelation of Jesus Christ, thus qualifying him to be an apostle.
John's Gospel came much later, decades after the other gospels had been written. John's Gospel is different in many ways. His purpose in writing it was not just to give another record of the life and acts of Jesus Christ, but "that you might believe that Jesus is the Christ, the Son of God, and that believing you might have life through His name." (John 20:31) John's record contains little that mirrors the other Gospels, rather John chooses to expand the record, giving us particular detail of events, especially of the Passion Week, not given in the Synoptic Gospels.
Understanding all that, now let us look at the three accounts of the last words of Christ.
Mat 27:46 And about the ninth hour Jesus cried with a loud voice, saying, Eli, Eli, lama sabachthani? that is to say, My God, my God, why hast thou forsaken me?
Mat 27:47 Some of them that stood there, when they heard that, said, This man calleth for Elias.
Mat 27:48 And straightway one of them ran, and took a sponge, and filled it with vinegar, and put it on a reed, and gave him to drink.
Mat 27:49 The rest said, Let be, let us see whether Elias will come to save him.
Mat 27:50 Jesus, when he had cried again with a loud voice, yielded up the ghost.
Mat 27:51 And, behold, the veil of the temple was rent in twain from the top to the bottom; and the earth did quake, and the rocks rent;
Mar 15:34 And at the ninth hour Jesus cried with a loud voice, saying, Eloi, Eloi, lama sabachthani? which is, being interpreted, My God, my God, why hast thou forsaken me?
Mar 15:35 And some of them that stood by, when they heard it, said, Behold, he calleth Elias.
Mar 15:36 And one ran and filled a spunge full of vinegar, and put it on a reed, and gave him to drink, saying, Let alone; let us see whether Elias will come to take him down.
Mar 15:37 And Jesus cried with a loud voice, and gave up the ghost.
Mar 15:38 And the veil of the temple was rent in twain from the top to the bottom.
Luk 23:44 And it was about the sixth hour, and there was a darkness over all the earth until the ninth hour.
Luk 23:45 And the sun was darkened, and the veil of the temple was rent in the midst.
Luk 23:46 And when Jesus had cried with a loud voice, he said, Father, into thy hands I commend my spirit: and having said thus, he gave up the ghost.
Joh 19:26 When Jesus therefore saw his mother, and the disciple standing by, whom he loved, he saith unto his mother, Woman, behold thy son!
Joh 19:27 Then saith he to the disciple, Behold thy mother! And from that hour that disciple took her unto his own home.
Joh 19:28 After this, Jesus knowing that all things were now accomplished, that the scripture might be fulfilled, saith, I thirst.
Joh 19:29 Now there was set a vessel full of vinegar: and they filled a spunge with vinegar, and put it upon hyssop, and put it to his mouth.
Joh 19:30 When Jesus therefore had received the vinegar, he said, It is finished: and he bowed his head, and gave up the ghost.
So, a comparison of the different passages sheds much light on the subject. Matthew and Mark both mention that Christ was given vinegar (most likely sour wine) to drink, he then cried with a loud voice, and then died. Luke makes no mention of the vinegar, but says that when, or after, Christ had cried with a loud voice, He then said, "Father, into your hands...", and then died.
Along comes John. He has no interest in retelling the exact same thing as given in the other Gospels, but rather gives us details missing in the other accounts. The other Gospels do not tell us that Christ put the care of His mother into the hands of John. The other gospels do not mention that Christ, prior to being offered the vinegar had said, "I thirst." All three other gospels mention that Christ had cried out with a loud voice, and here John fills in the blanks by giving us Christ's exact words, "It is finished!"
So, what happened? Matthew and Mark tell us that Christ cried out in a loud voice, "My God, my God, why have you forsaken me?" John tells us that Christ puts His mother Mary into John's care. John tells us that Christ, knowing that the Scripture had been fulfilled said, "I thirst." Matthew, Mark and John tell us that someone gave Jesus vinegar to drink. Matthew, Mark and Luke tell us that Jesus cried out for a second time in a loud voice, and John tells us that when Jesus cried out, He said, "It is finished!" Luke tells us that when, or after Jesus had cried out, He then said, "Father, into your hands I commit my spirit." Jesus then died.
Luke and John are not contradictory. They are complementary. When you understand the purpose for the writings of the different Gospels, you will see that even though they all may be talking of the same event, they may tell the story differently. All the details in each individual account are true, and when studied in parallel, you then see the complete picture.