In Skakel, the issue was the statute of limitations:

The legislature in 1975 passed a law that imposed a five-year statute of limitations, or deadline, for prosecuting all crimes, except those punishable by death. The following year the legislature passed an amendment specifically exempting from the five-year statute of limitations all Class A felonies, including murder. The amendment took effect April 6, 1976 - nearly six months after Moxley was killed.

At issue in the 1983 state Supreme Court ruling was whether the amendment applied retroactively. The court ruled that it didn't, when it upheld the dismissal of murder and other felony charges filed against Wilbur Paradise in 1981, for a 1974 incident. "Upon reconsideration, we are persuaded that Paradise was wrongly decided," Palmer wrote in the Skakel decision. Chief Justice William J. Sullivan and Justices Joette Katz, Christine Vertefeuille and Peter T. Zarella concurred.

At the time Martha Moxley was murdered, there was a five year statute of limitations in effect. In order to get around it and affirm Skakel's convction, the Court reversed its prior ruling of more than 20 years standing that an amendment excluding murder from the time limit could not apply retroactively.

If the defendant was a Joe Schmo no one ever heard of, would the decision have been the same? Or did the court want to affirm Skakel's conviction so badly it was willing to reverse it's own precedent to do so?

Anyone who believes Sam Alito would not do the same thing in an abortion rights case is fooling themselves.

The 89 page opinion in Skakel is here. (pdf)