Continuity mistake: In "The Luminous Fish Effect" (S1E04) Sheldon tells Penny he weighs 140 pounds. In "The Porkchop Indeterminacy" (S1E16), he tells his sister he weighs 165. 25lbs difference would be a noticeable change, but he looks the same.
Suggested correction: Lying to Penny but not to his sister, not inconsistent with the characters and his relationships.
The Big Bran Hypothesis - S1-E2
Continuity mistake: When Leonard and Sheldon are pushing the box up the stairs, the position of the box on the stairs changes instantly. In one shot it is flush against the wall, then in the centre of the stairs. (00:05:20)
The Big Bran Hypothesis - S1-E2
Continuity mistake: When shifting the box along the floor of the 3rd floor landing, Leonard's grips on the box is constantly changing. (00:06:00)
The Big Bran Hypothesis - S1-E2
Continuity mistake: When Sheldon is cleaning, he moves an iPod dock and the iPod lights up. Camera changes and the iPod is unlit. A few shots later it's lit again. (00:09:00)
The Big Bran Hypothesis - S1-E2
Continuity mistake: When cleaning Penny's apartment, Sheldon is holding up a jacket. Camera cuts and he is no longer holding the jacket up. (00:09:50)