To add, here's a summary from another of his talks on the same subject:
In the last 150 years we've discovered a lot of very old manuscripts. In those newly discovered manuscripts, we have found zero new readings of the Bible. All we've done with them is to confirm which of the readings we already have is more likely to be the original - which explains some of the differences in each translation of your Bible - some of them more modern, some more ancient. We're not getting new readings, we're confirming old ones - we're just getting more confident about the original text. Has the Bible been changed so much by scribes that we cannot recover its original text? No - it has been copied by scribes so much that they can't hide the original text. It was copied so early and so frequently that you can't hide what it said - you can't change it, you can't remove it. There's no reason to doubt that we have the Word of God handed down to us faithfully.
Differences between translations of Scripture will be subtle and ultimately don't change the original meaning of the text.
For example, here is the Parable of the Lost Coin (Luke 15:8-10) in four different English translations:
Either what woman having ten pieces of silver, if she lose one piece, doth not light a candle, and sweep the house, and seek diligently till she find it?
And when she hath found it, she calleth her friends and her neighbours together, saying, Rejoice with me; for I have found the piece which I had lost.
Likewise, I say unto you, there is joy in the presence of the angels of God over one sinner that repenteth. - King James Version
“Or what woman, having ten silver coins, if she loses one coin, does not light a lamp and sweep the house and seek diligently until she finds it? And when she has found it, she calls together her friends and neighbors, saying, ‘Rejoice with me, for I have found the coin that I had lost.’ Just so, I tell you, there is joy before the angels of God over one sinner who repents.” - English Standard Version
“Or suppose a woman has ten silver coins and loses one. Doesn’t she light a lamp, sweep the house and search carefully until she finds it? And when she finds it, she calls her friends and neighbors together and says, ‘Rejoice with me; I have found my lost coin.’ In the same way, I tell you, there is rejoicing in the presence of the angels of God over one sinner who repents.” - New International Version
“Or suppose a woman has ten silver coins and loses one. Won’t she light a lamp and sweep the entire house and search carefully until she finds it? And when she finds it, she will call in her friends and neighbors and say, ‘Rejoice with me because I have found my lost coin.’ In the same way, there is joy in the presence of God’s angels when even one sinner repents.” - New Living Translation