This passage appears in the account of Jesus visiting the house of Simon the Pharisee. The alleged error of the KJV rendering is that it supposedly says the woman is forgiven because she loved much. This makes "loving God" the cause for forgiveness--and salvation by implication--although the Bible says grace through faith is the means to salvation (Ephesians 2:8). However, the construction that appears in the KJV, along with the ESV and NASB, is what you would get from literally translating the sentence. The word at issue is "οτι (hoti)" which literally means "for" or "because". Thus it is correct to have "for she loved much". The supposed problem is that "for" or "because" are causative conjunctions, and it is unbiblical to make "loving much" the cause for forgiveness. For this reason some translations such as the NIV 2011 and NLT interpret "οτι (hoti)" as an evidentiary conjunction, which renders the following clause not so much the actual cause but rather the evidence of the result. This is what the NIV 2011 rendering of "as her great love has shown" attempts to do.
"Wherefore I say unto thee, Her sins, which are many, are forgiven; for she loved much: but to whom little is forgiven, the same loveth little." (Luke 7:47, KJV)
"Therefore, I tell you, her many sins have been forgiven--as her great love has shown. But whoever has been forgiven little loves little." (Luke 7:47, NIV 2011)
Critics of the KJV rendering are mistaken because they misread the verse. In the verse, the Lord is not saying that the woman is forgiven because she loved much. Rather, the Lord is saying that he is telling Simon that the woman is forgiven because she loved much. This is a subtle point but an important one:
The incorrect reading erroneously links the cause to the woman's forgiveness. But in Luke 7:47 the word "wherefore" (therefore), which introduces the entire resulting clause, precedes not only the phrase, "Her sins, which are many, are forgiven" but rather the whole of "I say unto thee, Her sins, which are many, are forgiven". Thus the result caused by "for she loved much" is not the woman's forgiveness, but rather Jesus' expressed positive judgment about the woman that she is forgiven. In essence, Jesus is saying that he can make a positive judgment about the tree (a positive judgment about the woman) because of her positive fruit (her love). It is because the woman loved much that Jesus was able to say to Simon that the woman was forgiven much - not that the great love caused the forgiveness. It is certainly biblical for the exhibited fruit to cause an observer to express a judgment about the tree, and this is the meaning of Luke 7:47. This concept had been taught in just the previous chapter in Luke 6:44. There is no error here in the KJV, ESV or NASB.