Continuity mistake: Near the end of the episode, in the canteen scene, Howard shows the card trick to Sheldon again. The card at the bottom of the deck is the 2 of hearts as he takes them from the box. Sheldon then takes this card from near the top of the deck when Howard puts them on the table. The deck is not shuffled between times.
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.
Character mistake: Even with Penny and Zack the guys are one man short to be the original JLA because they they don't have the Martian Manhunter. If they used the same costumes in the previous year, they would have been three people short of the original line-up.
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.
Revealing mistake: Near the end of the show, the big robot is chasing the other robot down the hallway. The camera starts to zoom in as the robots come by it. The big robot stops just before the camera zoom is past it, yet they keep running down the hallway like the robot is still going.
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Continuity mistake: When Sheldon goes to speak to Leonard, he is sitting on the couch. Camera cuts to Raj for one second, then to Penny and you can see Sheldon has crossed the apartment and is now in the hall. There is not enough time to move that far in that time.
Character mistake: As they drive to Todd Zarnecki's to confront him, Sheldon says, "I almost feel sorry for the poor fool, sitting in his split-level suburban ranch..." Architecturally, split-level (technically three levels joined by half flights of stairs) and ranch (single level) are separate and distinct designs. There is no "fusion" of the two. I can't help but think Sheldon would have corrected anyone who said the same thing.
Continuity mistake: In the scene where Leonard is packing up his collectables to sell, at 15:32 he is dusting what appears to be a Hasbro Marvel Legends Yellow jacket figure, which also has a yellow post-it on the back. At 15:42 he is still dusting a figure but he now holds a different (darker but not yellow) figure from the same series, with no post-it on the back, and the Yellow jacket figure is now on the table (house left of the box of collectables). At 15:56 The Yellow jacket figure has disappeared from the table, and it is not the figure in Leonard's hands either.