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.
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.
Other mistake: In the scene where Leonard threatens to open his production era, we see the Star Trek The Next Generation Geordi LaForge (w/o visor) action figure. The uniform worn by the action figure is only worn by Geordi in Star Trek Generations the movie, not the television series.
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. (00:15:30)