The pan Alex uses to cook the lasagna is a type developed for baking brownies. The shape was designed to ensure every brownie was an "edge piece".
Everyone calls Draper "Gunny". Gunnery Sergeant is a Marine rank between Staff and Master Sergeant. Gunnies will command squads or platoons in the field. While the nickname "Gunny" is a sign of respect and affection, lower ranks sort of need permission to use it.
The device that is on the table in the Med Lab (to Naomi's right) is a Millipore water purification system ("MilliQ"), which is often used in Biochemistry labs. The ultrapure water produced is much, much purer than distilled water.
The Marines speculated how much money the family of Pvt. Hillman ("Hill") has. The real-life Hillman Family Foundations have been active since the 20th century and their gifts include the Hillman Cancer Center and the Hillman Library at the University of Pittsburgh.