"It matters little about the mother's credibility."
I'm sorry, I think you are wrong. She's a major witness in this trial, her credibility matters a lot. It seems like they've made a major error in putting this easily impeachable woman on the stand, and it seems like the step-father wasn't too much better.
Now, the Peterson trial seemed to be going very badly for the prosecution also, and they got a conviction (total conviction actually) at the end, so the prosecution may ultimately be successful in this trial. But I don't think you can say that it doesn't matter what this woman says, if that were the case she wouldn't be on the stand to begin with.
What about the evidence the prosecution has produced that prove most of what she said was true?
Again the problem is guaranteed to happen. No sane parent would have left their kids with a known child molester. So you are guaranteed to have witnesses who are warped. I would be happy to be a witness but I would never set foot within a mile of Jackson and his pedophilia palace and would not allow my son within five miles of it. People like me would be credible witnesses but since we don't get involved in these situations it is of no use.
Pundits on Fox and MSNBC both stated that her story would be incredible except there is supporting evidence such as surveillance videos of her and her family that were seized at the private eye's office. The private eye Jackson had hired to watch them.
There was other evidence along that line that buttressed her testimony.