I think that Berman is not allowed to dispute the evidence or Goodell's interpretations of the evidence. So (for example) if Goodell says science doesn't show Brady didn't deflate or even that there's little evidence deflation happened at all, Berman cannot substitute his opinion for Goodell's.
However, I think that Berman is allowed to consider the quality of the evidence and Goodell's interpretations of it for purposes of deciding if Goodell is acting in a sufficiently arbitrary, unfair, biased way.
But I (like many of us, I'm sure!) would love to hear from someone with legal experience re: the Federal Arbitration Act about where the lines are between a judge incorrectly reopening issues of fact and analyzing fairness of process.