The woman, whom Peterson had just met, said that she tried to talk about other things such as business, but that he kept turning the conversation to sex.
He was obviously trying to initiate a sexual relationship with this woman that he'd just met.
In doing this, he was cheating on his wife.
Cheating on one's wife is dishonest.
Scott has made statements that he had "nothing to do" with the murder of his wife.
Those statements will come in as evidence in this trial.
If the prosecution wants the jury to not believe Scott's denials, then it needs to show that he is dishonest. Showing that he was cheating on his wife = showing that he was dishonest.
Think of it this way: A president cheats on his wife. Knowing this, it does not surprise you as much when you are asked to believe that this president also committed perjury, which = LYING.
If, OTOH, you think the Clinton impeachment was "just about sex", then please disregard all of the above.
If he lies, then he is a murderer. Not!