Factual error: Sheldon tries to pretend that it is 2003, before he met Leonard. But in the episode The 21 Second Excitation S4 E8 it was stated Leonard and Sheldon waited in line for 14 hours to see the midnight premiere of Star Trek: Nemesis. Star Trek: Nemesis premiered on the 9th of December 2002.
Continuity mistake: Sheldon is returning Amy's scarf and says, "You wore it the night we went ice skating, remember?" to which Amy replies, "You mean the night that I went ice skating and you stood at the rail Googling the symptoms of hypothermia." But in episode 8-12: The Space Probe Disintegration, Amy states that she cannot go ice skating because she has "unnaturally brittle ankles." (00:04:55)
Continuity mistake: In episode 16 of season 1, Penny is talking about making a cake for Leonard's birthday and states she knows his birthday because she was checking a horoscope for him. But in this episode she does not know when his birthday is, which leads to Leonard revealing he was secretly reading Penny's diary. (00:40:00)
Continuity mistake: In the first half of the episode while in Las Vegas, Penny's hair is short; however, later in the episode when she is back in the apartment speaking with Sheldon, her hair is much longer, albeit tied back in a bun, but very obviously much longer and a very different color. The scene from Las Vegas to her apartment was less than 24 hours apart and would have been impossible for her hair to have grown so much.