Character mistake: Sheldon is a well-documented and self-proclaimed germophobe. It is completely out of character for him to retrieve the bag of chicken from the trash.
Continuity mistake: Sheldon puts the bag in the bin at the start of the episode so that the handles are facing the ground. When he gets the bag out, the handles are at the top of the bin.
Audio problem: When Sheldon is knocking on Leonard's door at the start, the sound is out of sync with the action.
Continuity mistake: When Penny is telling Howard and Raj about Sheldon's "drug addicted cousin" her scarf keeps jumping in and out of her jacket.
Continuity mistake: In nearly every episode, Sheldon demonstrates his OCD when he knocks three times on a door, says a person's name, and repeats that sequence twice, for a total of three iterations, but in this episode he radically departs from that behavior not once but twice. First, wanting to talk to Leonard, he knocks four times, says "Leonard" and repeats the sequence three times for a total of four iterations. Later, wanting to talk to Penny, he knocks four times and says her name, repeating that sequence at least four more times. Given that this was the first season, I assume the writers had not yet settled upon the 3x3 routine as a comic behavior.
Continuity mistake: During the whole opening scene, the way in which Leonard holds the letters in his hands keeps differing.
Continuity mistake: When Sheldon is talking with Leonard in the kitchen at night, as he pours himself a mug of milk the mug moves between shots. (00:04:50)
Continuity mistake: Sheldon puts the bag of takeout into the lobby trash can and as he does so, the whole bag turns sideways. At the end of the scene, he takes the bag out of the can and it's upright without him turning it.
Other mistake: Leonard says that it's 2am when his door is knocked on, but when he opens his door to confront Sheldon, his window outside shows daytime light. (04:12:00 - 04:25:00)
