He is the only pure special teams player to win the Sporting News’ NFL MVP award and is one of only three non-offensive MVPs.

He spent two years out of the NFL and moved back to Livingston, Texas, where he installed septic systems and coached high school sports.

[5][7] With the retirement of the Minnesota Vikings' Rick Danmeier in 1982, Moseley became the sole full-time straight on placekicker in the National Football League; there has only been one other (Dirk Borgognone, who played two games in 1995) since then.

[9] He became the first placekicker to ever win the Associated Press NFL Most Valuable Player; (Hall of Famer Lou Groza won the Sporting News NFL Player of the Year Award in 1954 as a placekicker and offensive tackle, followed by George Blanda winning the same as a kicker and quarterback in 1970.

But in the Washington Redskins' 27–17 victory in Super Bowl XVII over the Miami Dolphins, Moseley kicked two field goals and was successful on all three of his extra point attempts.

He signed with the Cleveland Browns and retired at the end of the season, helping them win their divisional playoff game against the New York Jets with a game-winning field goal in double overtime despite missing two field goals in regulation and another in the first overtime period.

After the killing, Moseley was extremely critical of the criminal justice system's treatment of Penry, who was released after serving two years of a five-year sentence for rape months before the murder took place.