Francis Beckwith, author of the important and learned Defending Life: A Moral and Legal Case Against Abortion Choice (Cambridge University Press, 2007), writes:
It is no exaggeration to say that no U.S. Supreme Court opinion has been more misunderstood and has had its arguments more misrepresented in the public square than Roe v. Wade (1973). There seems to be a widespread perception that Roe was a moderate opinion that does not support abortion on demand, i.e., unrestricted abortion for all nine months for virtually any reason. . . .
In order to fully grasp the reasoning of Roe, its paucity as a piece of constitutional jurisprudence, and the current state of abortion law, this article looks at three different but interrelated topics: (1) what the Court actually concluded in Roe; (2) the Court’s reasoning in Roe; and (3) how subsequent Court opinions, including Casey v. Planned Parenthood, have shaped the jurisprudence of abortion law.
You can read online the whole analysis: “The Supreme Court, Roe v. Wade, and Abortion Law.”
For shorter summaries of the serious flaws in the legal reasoning, see Beckwith’s blog posts on (1) The Court’s Failure to Address the Question of the Unborn’s Moral Status, and (2) The Court’s Two Unwarranted Stipulations.