The "shelf" Howard (Simon Helberg) is building is actually an inverted Kodiak Sidewinder motorized step (painted silver), used for entering/exiting lifted trucks.
When Dennis Kim (Austin Lee) enters Sheldon (Jim Parsons)'s office, his whiteboard features a massless two-loop self-energy diagram and the evaluation of the associated multiloop Feynman integral. Multiloop Feynman integrals appear when quantum-field amplitudes are constructed within perturbation theory. They are integrals over so-called loop momenta. Feynman integrals are usually complicated objects even in a one-loop approximation, so that the number of loops equal to two is already considered big.
Sheldon (Jim Parsons)'s comment about Dennis (Austin Lee) seeing The Matrix (1999) supposes that Dennis Kim is able to detect the "real" reality, from which the movie series takes its name, in which mankind is actually enslaved by machines who live off of human body heat and electrochemical energy. Most people, as depicted in the series of movies, are in a sort of state of hypnosis, living an artificial reality imposed on them.
Leonard (Johnny Galecki) says "A bad feeling I have about this!" doing a Yoda impression. The line "I have a bad feeling about this" is said in every episode of the main Star Wars series, although Yoda (also from Star Wars) would probably have said "A bad feeling about this I have!".
This episode was watched by 7.69 million people with a rating of 2.8 (adults 18-49).