In The Friendship Contraction (2012) Sheldon says that he needs to go to Supercuts to get his haircut. However, in The Werewolf Transformation (2012) he says that he goes to a barber shop to get his haircuts.
Around 11:45, Penny smiles at Leonard with her mouth closed. It then cuts to a different angle and Penny can just be seen on the right with her lips parted and her teeth showing.
Penny and Leonard show up at Amy's apartment to find Sheldon sleeping on her couch. However, his head is closest to the door, which goes against his own instructions from The Dumpling Paradox (2007) where Sheldon explains to Penny that she should sleep with her head away from the door for safety.
Sheldon states that his hair grows at the rate of 4.6 yoctometres per femtosecond. This is an incorrect use of SI units. Multiples and submultiples should not be combined in derived unit. The correct quantity is 4.6 nanometres per second.