Kulpa was head-butted by Carl Everett of the Boston Red Sox in 2000 during an argument about the location of the inner boundary of the batter's box.

On August 12, 2013, he ejected Rangers catcher A. J. Pierzynski for arguing a ball three call during pitcher Yu Darvish's bid for a perfect game against the Houston Astros.

The perfect game was broken up moments later on an ensuing ball four pitch to Astros batter Jonathan Villar.

[3] On April 8, 2021, Kulpa made a controversial call as the home-plate umpire of a game between the New York Mets and the Marlins.

"[4][5] Kulpa was the home plate umpire when Detroit Tigers pitcher Justin Verlander threw a no-hitter at Comerica Park vs. the Milwaukee Brewers on June 12, 2007.

[7] Kulpa was the first base umpire on July 9, 2011, when Derek Jeter of the New York Yankees got his 3000th career hit against the Tampa Bay Rays.

[8] On September 13, 2020, Kulpa was the first base umpire for a no-hitter thrown by Alec Mills of the Chicago Cubs against the Milwaukee Brewers.