When they talk about how vampires shave when they can't see themselves in the mirror, that they meet in pairs and shave each other is wrong. Vampires are dead and don't need to shave because hair doesn't grow when you're dead.
Incorrectly regarded as a goof - Leonard added CoffeeMate to his coffee. CoffeeMate is a non-dairy, lactose free creamer, so Leonard would have no problem consuming it.
The background seen behind Amy when she video-chats with Sheldon shows a completely different layout with different furniture than what is seen in her apartment later during the series. However, most video chat programs allow the user to change the background to show any kind of picture - in The Thespian Catalyst (2011) Amy's background was the inside of a fish tank, and she changed it with one click when Sheldon didn't find it amusing.
When Leonard said Dr. Siebert is 12 o'clock, he really should have said 9 o'clock for him and Sheldon and 3 o'clock for Raj and Howard based on how each of them are sitting.