The question Has Perelman's proof been accepted or are there still unresolved issues? has been closed as of this writing. At first glance, this question seems to be of the genre, "Is this paper about a famous problem correct?" which the MO community has long ago decided is off-topic unless specific technical issues are spelled out in the MO question. However, this question is slightly different. It is not directly asking about Perelman's paper; it is asking about a statement published by Shing-Tung Yau, raising doubts about whether Perelman's argument has been fully checked.
Complicating the matter is that Yau's comments are, by his own admission, phrased in a controversial ("subjective and argumentative"?) manner. That initially influenced me to agree with those who voted to close (although I myself did not vote to close). However, the MO question itself does not strike me as subjective and argumentative. The MO question seems more in line with questions such as Extent of “unscientific”, and of wrong, papers in research mathematics, which asks about whether published and "generally accepted" papers are really as rock-solid as the mathematics community would like to believe. In a comment, arsmath wrote:
I'm not trying to defend Yau, since the consensus is that he's wrong. I am trying to defend the principle that asking the question is legitimate. I don't see any way to interpret what happened here other than we as a community have decided to cover up any embarrassing fights. Which, to my mind, is more embarrassing than the fight itself.
I think that arsmath has a valid point. Note that an earlier comment by GH from MO, affirming the legitimacy of the MO question, has been upvoted 10 times as of this writing. Even before arsmath's comment, I had cast the third vote to reopen the question. Those reopen votes seem to have expired, and since the question isn't currently active, the only realistic path to reopening seems to be a post here on meta.
If the question were reopened, I would try to answer it by saying that the correctness of a paper, especially one containing a very complicated argument, is not a simple binary question, but lies on a continuum. It is not unreasonable to draw attention to a published argument and suggest that it should be scrutinized by more people, digested properly by the community, and generalized or adapted to other problems if possible. The trouble is that Yau has gone about this in an intentionally tactless manner, making Perelman's work seem more doubtful than it is, and courting controversy while disingenuously claiming to care only about the math. In my answer, which I would make community wiki, I would also reproduce the mathematical content of some of the comments, which cite recent work that builds on Perelman's ideas.