This isn't my area, but I know enough to say that he speaks the right language and builds on existing results in the field.

So I'd classify this as a serious contender... in the same sense as other serious contenders have been put forward every 1-2 years for the past 50 years, only to be withdrawn after someone points out mistakes. I'd say that it's almost certain that there are mistakes somewhere in this paper -- the only question is whether they're serious flaws or just minor errors which can be worked around.

The author has this named after him. http://en.wikipedia.org/wiki/Li%27s_criterion

I know enough to know the author believes it to be a serious contender. At least it's not some kind of joke.