Revealing mistake: When Sheldon goes to Penny's apartment and they do a scene study together, they both read lines from a multi-page script that Sheldon brings with him. On a couple of occasions the camera cuts to a side view of Sheldon and we get to see the page of the script that he's currently reading from. The pages are completely blank.
Revealing mistake: In the scene where Leonard is supposedly playing Halo 3 against somebody in Copenhagen, there is no ethernet cable or wireless adapter connected to the Xbox 360 (one of the originals without wireless inbuilt), which means that there is no way he can be playing online with someone in another country.
Revealing mistake: Sheldon's laptop has gone through several strange transformations throughout the series, but in this episode it takes the biscuit - it appears to be a Dell XPS with the back covered up, but the shot of Sheldon chatting only to Amy shows a Mac keyboard, with the laptop running OS X.
Revealing mistake: If you look at the marble patterns on the walls, they are all exactly the same from floor to floor. Also the bricks oddities on the stairway match from floor to floor. They change lights, elevator tape etc. but it's the same floor used over and over as different floors.
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Revealing mistake: Throughout the series much is made of the fact that Howard's mother is grossly obese, and in The Engagement Reaction (S4 E23) it is even mentioned that her arms are hugely oversized. However, at the end of this episode we see her arms when she grabs Raj to stop him climbing out of the window, and they are the arms of an average-weight woman - they aren't overweight at all.
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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