Continuity mistake: The Stevenson Award in Sheldon's office reads "Sheldon Cooper, PhD." But, in the "Dennis Kim" episode we are told Sheldon was 14.5 years old when he earned that award - 1.5 years before earning his PhD at age 16, so the award should not show the title of PhD.
Continuity mistake: In the scene where Howard and Raj are comparing the size of their breast area, Bernadette is seen in the background holding a mug with the handle in her right hand. However, when the scene zooms in on her, the handle appears in her left hand.
Continuity mistake: When Sheldon and Mike are drunk on the couch after Howard leaves, they are toasting with the beer cans. Sheldon has his in his right hand, but when Bernardette came in, the can is in his left. A little bit later, after he says "she's so tiny", the can moves back to his right hand.
Revealing mistake: After Howard lets go of the unpacked treadmill, it begins to fall down the stairs. As it goes out of frame, the treadmill begins to level itself out, but the sound of it is still heard falling and Howard, Bernadette and Raj continue running past, way further than where it levelled itself out anyway.
Continuity mistake: At the end of the episode when Lennard asks Sheldon about his train ride, he says that he kissed Amy on the lips, and says that it tasted like the brownies that they had that for dessert. But they were eating a tart of some type, with a shortbread crust. No brownies were on the table.