Quick thing: believe it or not, the NFL actually caught a lucky break from Judge Berman.
He chose not to rule on the evident partiality argument (basically Goodell's bias as arbitrator). Brady had already won the case and didn't need it. Also, the no notice & discovery issue points are solid enough to affirm the Judge's decision on appeal.
If the Judge ruled on Goodell's bias and it went Brady/the NFLPA's way, it would essentially mean re-writing the CBA and effectively stripping down Goodell's power. The NFL and NFLPA would have needed to figure out an alternative immediately after this case for future disciplinary matters.
So basically…Goodell still gets to play prosecutor/judge/jury/executioner if he really wants to. It's up to the owners to make a change since the court didn't rule on it.