The Electric Can Opener Fluctuation - S3-E1
Continuity mistake: Sheldon's Sandwich goes from looking burnt to not burnt in the next few frames. (00:16:56)
The Transporter Malfunction - S5-E20
Continuity mistake: Sheldon opens his transporter box and takes out Mr. Spock, while making a big deal about it remaining mint in box, unopened. Later, he makes a big show of using an exacto knife to gently open the box with Spock in it.
The Vengeance Formulation - S3-E9
Character mistake: When Leonard, Sheldon, and Raj are watching Kripke entering his office with the board of directors, Kripke says "President Siebert", yet Siebert is not among the people standing with him.
Chosen answer: It does. The variable cleanliness of the cab and the habit of taxi drivers to engage customers in small talk would be too much for Sheldon to handle, and not an option for him.
Captain Defenestrator