I have no labor law experience -- well, very little. The NFL's argument makes sense to me. The CBA is set up so that I impose conduct detrimental discipline, and it also allows me to sit on "any appeal." That's what I'm doing. There is no inherent conflict of interest. If the PA wanted to collectively bargain for a different arrangement, it should have. It didn't.
The NFLPA is free to argue in any case that I'm biased, but I don't think I am. And you don't have evidence that I am. [Good luck trying to win that one in court.]
The Vincent issue is a red herring to me. A big nothing. Even if one might argue that the discipline was, initially, Vincent's, Goodell has now owned it. Whatever confusion there might have been in the past, Goodell is now saying it's his discipline. Maybe one can make a procedural argument that he should have done that earlier, but he's done it now, and so if there ever was a problem I think he's fixed it. Brady has three weeks to prepare, so even any argument he might have made that he would prepare different if he knew it was Goodell's discipline not Vincent's is out the window.
It's fucked up that Goodell gets to impose discipline and then hear an appeal from the discipline he imposed. Maybe there's grounds to say it's inherently problematic, since there is a general principle in anglo-saxon law against it. When there's a Latin phrase for it, you know it's serious. (Nemo iudex in causa sua -- no man should be a judge in his own cause.) Unfortunately, that's what the CBA provides. It's hard to imagine a judge saying that a collectively bargained alternative dispute procedure is inherently void.
If I were the NFL I would argue that there is no requirement for any appeal. If the parties had wanted to, they could have agreed that commissioner discipline is final. They didn't, but since they could have, there is nothing wrong with bargaining that the commissioner decides an appeal.
I think the fact that Goodell is reviewing his own discipline will be helpful to the NFLPA/Brady -- it will probably give any other errors they raise more traction since there will likely be some judicial skepticism, but I really don't see how it, standing alone, is a silver bullet.