What is the most common misconception people have about JWs?
That they don't believe in Jesus. JW's don't put nearly enough emphasis on Christ and have missed out on what it means to have a relationship with him, but they most certainly do believe in Jesus and view him as their redeemer and they even acknowledge he is the divine Logos. They just feel that Jesus is always a lesser God than the Father and that it is to the Father alone that we should render sacred service.
What is the most common misconception that JWs have about Christians?
That they are all a part of a Satanic controlled empire of false religion and that those in such false religions will most likely die because they believe in the trinity and a few other doctrines that JW's reject.