It's only once every four years that we have a February 29, and it's unsurprisingly rare for your favorite baseball team to have much in the way of history on the date. In addition to the infrequency with which the date appears on a calendar, it's a day that falls in the early stages of spring training—an uncommon time for a team to make major news.
The New York Mets haven't done much of note on February 29 in the past. Casey Stengel appeared on the front page of The Sporting News on February 29, 1964, and that issue is available for sale on Amazon. And on February 29, 2000, the Newark Bears invited—by way of a press release—former Mets slugger Darry Strawberry to play for them after he was suspended for a year by Major League Baseball.
It's fitting that the best connection to the Mets have to the date belongs to an outfielder who made three plate appearances for the team in his major league career: Terrence Long. The Mets' first-round pick in the 1994 amateur draft, Long was born on February 29, 1976, worked his way up the team's minor league ranks and a good year in Double-A Binghamton in 1998, his age-22 season. Long spent the grand majority of his season in Triple-A in 1999, but he made three plate appearances, each one a pinch-hitting appearance, for the major league Mets in the first few weeks of that season.
In late July, the Mets traded Long and minor league pitcher Leo Vasquez were traded to the Oakland A's for starting pitcher Kenny Rogers, who was in his age-34 and had a 4.30 ERA—which was better than league average back then—at the time. Long went on to play for the A's for four years before spending one season each with the Padres, Royals, and Yankees. Rogers had a 4.03 ERA in twelve regular season starts for the Mets, and both his and the team's seasons ended when he issued a walk-off walk that sent the Atlanta Braves to the World Series. Rogers left via free agency following that postseason departure, which was probably for the best.
In conclusion, happy birthday, Terrence Long!