Before joining the force, Elliot Stabler served in the U.S. Marine Corps. His tattoo, which depicts the Marine Corps emblem, is often shown. In the Season 6 episode "Goliath," Detective Munch mentions that Stabler served in Operation Desert Storm. But that makes no sense, as Stabler was already a detective by then. Operation Desert Storm was a 42-day offensive which took place in 1991. According to Season 1's "Wrong is Right," Stabler had already joined the police force by the time 1986 rolled around, and became a detective in 1992. What gives?
It's possible that Stabler went from the Marine Corps to the force, then signed back up briefly for Desert Storm. Harry Bosch did something similar on "Bosch" by leaving the LAPD to re-enlist in the U.S. Army Special Forces after 9/11. But Bosch was already a detective when he took his leave. Stabler made detective in 1992, which would have been very hard to do if he'd ducked out for a quick jaunt to Kuwait in '91.
Still, Stabler doesn't have the most confusing military history, as far as TV characters go: That honor probably belongs to Abe Simpson. Over the course of "The Simpsons," Grampa Simpson has claimed or been shown to have served in every branch of the U.S. Armed Forces. Well, except Space Force — but give it a season or two, and he'll get there.