Character mistake: In his conversation with Missy Sheldon makes it clear that his superior intelligence is a result of a random, mutated gene. Since Missy isn't similarly intelligent she obviously isn't carrying this mutated gene (which would be a billion to one shot anyway) so her offspring wouldn't inherit it. Sheldon would know this - his offspring would carry the mutated gene for superior intelligence, Missy's would not. Anyone knowing enough about genetics to use the term 'randomly mutated gene' understands enough to know that the mutated gene would only be expressed in a direct line from the carrier - Sheldon. Also bear in mind he has a model of the DNA molecule in his living room - it is obviously an interest.
Character mistake: In his argument with Leonard regarding Superman's ability to fly, Sheldon states that in Superman 1, Lois Lane is two feet off the ground when Superman catches her as she falls from the helicopter. Not so. Superman catches Lois at least ten stories up. Additionally, both Penny and Sheldon say Superman "swoops down" to save Lois. Penny can be forgiven, but Sheldon would know better: Superman flies UP from ground level to catch Lois. (00:02:30)
Continuity mistake: At the end when Sheldon has got a burger, the amount of burger left changes depending on the camera angle. Most noticeable when he asks Penny about permanently reserving the table - between shots the lettuce disappears, the bun changes colour, and the bite marks change.
Character mistake: Being the first to play in the "time machine," Leonard says he will set the date for March 10, 1876. Howard says "Good choice. Alexander Graham Bell invents the telephone and calls out for Doctor Watson." Bell's assistant, Thomas A. Watson, was an experienced electrical designer and mechanic, but he did not hold an advanced degree. It is well documented that the first words transmitted over the telephone identified him as Mister Watson.
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. (00:09:00)
Character mistake: Sheldon is wrong about the physics of pushing the furniture up the stairs. This is not just a question of work (energy) but also of power (energy/time). Since he and Leonard cannot produce an unlimited amount of energy per second, they may need to push it slowly, contrary to what he asserts. This is a very serious and very basic error for Sheldon considering he has a PhD in Physics.
Factual error: The time machine in this episode is supposedly the same one used in the H.G. Wells movie, but there are mistakes in the controls that would have been obvious to the characters: 1. When Leonard first gets into the machine he talks about traveling into the past and says something like "I'm setting the date to..." That is the method used to operate the Wayback Machine in the Rocky and Bullwinkle cartoon, but not the time machine in the H.G. Wells movie. Rod Taylor could not set the desired date on the controls, he simply used the lever to move forward and backward through time and the date display updated automatically to show the current date. 2. In the movie the default position of the lever was at a 45 degree angle. Pushing the lever forward moved the machine into the future, pulling back on the lever moved the machine into the past. In the TV show the default position of the lever is vertical and Leonard pulls the lever backwards to move forward into the future - opposite of the movie.