By most accounts, Roe itself is simply a "raw exercise of judicial power," and a poorly reasoned one at that. The Roe Court explains that the right of a woman to abort a child emanates from the Constitution’s “penumbra” of provisions guaranteeing individual liberty; complete poppycock, which if taken to logical conclusion, means nothing except that the Supreme Court, not the text of the U.S. Constitution, determines what is a fundamental constitutional right and what is not. This is a problem because the Supreme Court, like most tyrants, is inclined to fits of irrationality and unpredictability. Even Justice Ruth Bader Ginsburg, a Clinton appointee and supporter of abortion, has argued that Roe is a poor example of legal reasoning. (Ginsburg prefers upholding abortion on grounds of equality rather than liberty. See here.)
As you may have heard, Norma McCorvey, a.k.a. “Jane Roe”, is trying to have Roe overturned by asking the court to reopen her case in light of 30 years of experience and scientific development. Specifically, she wants the court to consider evidence on the sentience of the fetus and on the psychological risks to women who have had abortions and to find that these are sufficient justification--“a compelling state interest”--for allowing states to prohibit abortion. The Fifth Circuit Court of Appeals affirmed the lower court’s ruling that McCorvey’s effort is precluded by the mootness doctrine, which means that because Texas law no longer outlaws abortion, a decision in her favor would have no practical effect and cannot be considered; i.e., in the years since Roe, all anti-abortion laws have been repealed, including the one McCorvey sought to have overturned in 1973. Of course, this is a catch 22 because the abortion laws were repealed because of Roe. (For more on McCorvey’s case, see here).
Sounds stupid? Well, Judge Edith Jones, author of the Fifth Circuit’s decision, thought so too and chose to write a concurrence to her own opinion in which she railed against Roe and the odd procedural rules that allow the Court to avoid reopening Roe even if the facts have changed enough that Roe might not come out as it did if reheard today. (You can read the 5th Circuit’s decision, followed by Judge Jones’ concurrence, here [.pdf]. A media report on the decision and concurrence is here.) That said, unless the Supreme Court chooses to make an exception to the mootness doctrine, which it could, then McCorvey’s case will fail. Presently she is waiting on a ruling on her cert petition filed with the Supreme Court. It is highly doubtful that the court will even take the case, though one can never predict when it comes to tyrants.