Can Byakugan read mind?
Short Answer is: No, Byakugan cannot read anyone's mind. As to the episode that you are referencing, you need to keep few things in mind:

1) Hinata, during the Chunin exams( I think that's what they're called), was very predictible to begin with, and hence any decent ninja would be able to know her next move by looking at her stance.

2) Neji, with his Byakugan, can see Hinata's chakra-flow, and chakra-flow changes depending on the person's physical and mental state.

3) Neji was fighting Hinata, and it is a common tactic to say things to your opponent that will affect their confidence. If you watch the whole fight, once Hinata remembers Naruto and gains confidence, Neji stops bragging about reading her mind.

Also, Byakugan's ability to gain knowledge of person's mental state by reading chakra-flow, is not the same as reading minds because chakra-flow does not indicate anything about one's thoughts.