This is from a VERY specific perspective, and other perspectives are likely to have a different answer (and possibly take offense, though none is meant.)
From the perspective of my Fundamental, Independent Baptist Church, which regards the Bible ad God's word, written by men as inspired by the Holy Spirit, and therefore, inerrant and infallible. (Starting out rather legalistic and then getting realistic)
To worship in truth means to worship as God has revealed Himself to us. To not twist Biblical teaching and statements to distort their meaning.
- Some believe that God is a loving God, and would never send someone to Hell. They think that somehow, God will overlook their sins because of His love for him.
- From our point of view, this is not worshiping in truth, it's idolatry - making a god to suit ourselves, rather than accepting the hard truth that Hell is real, and that without the saving grace of Christ, all are doomed to an eternity there. The truth that god does allow us to spend an eternity in hell if we choose to reject Him in spite of His love.
- The Churches that teach such things, and the people that choose to follow them are teaching and following the doctrines and commandments of men, rather than those of God. (Matthew 15:8-9)
Of course, as evidenced on this site, "not twisting Scripture" is not such a clear thing. It is quite possible for two people to read the same Bible and come to vastly different conclusions about what it says.
One of the distinctive traits about us is that we hold very closely to the idea of sound doctrine. We probably emphasize it too much over love and being a light in the world through good works. But even among ourselves, there are things we don't agree on.
Still, I think that worshiping God, as He revealed Himself, to the best of our ability, is a good definition of worshiping in truth.