After Leonard unwraps the book, there is still some of the paper taped to the end away from him. This portion is later torn back without anyone touching it.
The shots of Bernadette looking at them singing to her are from a different take since Penny's hands are held differently when she is viewed directly.
When Sheldon looks at the book and discovers his mistake, the spreading of his left fingers changes between shots.
Amy mentions that the last time Sheldon was "in the zone", it was when he was figuring out electron transport in Graphene. That was in S3 E14, The Einstein Approximation. Amy's character wasn't introduced until S3 E23, The Lunar Excitation.
On Sheldon's whiteboard showing all of the electron configurations, there is a mistake in the equation written in red. Sheldon writes Uranium-238 as element 96, when it should be written as element 92. Elements are identified by the number of protons in the nucleus. Element 96 is correctly identified as Curium or Cm in the line above.
Sheldon uses the incorrect short-hand notation for element 118. Sheldon uses Uuo. Element 118 was discovered in 2006 and was changed to Og for Oganesson. This episode aired in late 2013, long after the change to the periodic table.
When Penny shows Leonard the letter that he wrote her after their first night together (all 11 pages of it), the pages are blank.
You can see typing on the paper at the end of the scene.
Sheldon takes a chocolate chip cookie from Leonard's tray in the cafeteria. Leonard is lactose intolerant so he wouldn't have a chocolate chip cookie since chocolate chips contain milk. Also, Sheldon wouldn't touch food that has been touched by another person.
Throughout the series, Amy is shown writing with her left hand. Strangely, here she writes with her right hand.