The medic and other soldiers all have name patches with names borrowed from producers, production staff and anyone else working on Alpha House.
"In the shit" refers to military slang for being in a firefight or otherwise engaging in combat. The phrase is often heard on military communications when a unit is seeking assistance. Soldiers are divided between those who have been "in the shit" and those who haven't. The former have more street cred and bragging rights.
Landstuhl Regional Medical Center in Landstuhl, Germany is a major U.S. Army hospital dating back to the U.S. occupation of Germany after World War II. Casualties are routinely flown there from combat areas in the Middle East for treatment.
"I voted to close Walter Reed" refers to a commission formed in 2005 to close and consolidate military bases voted to close Walter Reed Army Medical Center, a storied Washington, D.C. hospital where Gens. Dwight D. Eisenhower and Douglas MacArthur died and generations of wounded soldiers were treated. In 2011, the original Walter Reed shut its doors and patients were moved to Bethesda, Maryland where army medical personnel combined with a naval hospital to create the new Walter Reed National Military Medical Center.
Louise Laffer is played by Amy Sedaris, wearing a wig. She calls Louis "Little Giant," which was the nickname of Senator Stephen A. Douglas, Lincoln's opponent in the Lincoln-Douglas debates.