They didn't give him 1st degree for both his wife and his baby, because as the juror foreman stated they, "couldn't find any reason or evidence why he would have premeditated killing his wife." That alone should tell you that they didn't know what his motive was for killing his wife.
If you don't have physical evidence, shouldn't you have motive?
I see some motive in this case (the obvious motive of him wanting to be free etc.).
But the juror stated in his own words that he had no clue of what motivated Scott Peterson to kill his wife and thus is why "they" split the verdict to a 1st degree verdict and a second degree verdict.
Admitting that "they" couldn't find a reason as to why he would have done this, should make good grounds for whatever appellate lawyer is appealing his case.