When talking to Dennis Kim about the Stevenson Award (and Sheldon not being the youngest to ever win it), on Sheldon's certificate can be seen with the name "Sheldon Lee Cooper, Ph.D." Sheldon won the award at age 14-1/2; in the Cooper-Hofstader Polarization, Leonard states than Sheldon received his Ph.D at age 16 - so the Stevenson Award could not refer to Sheldon as doctor.
When Sheldon approaches Leonard telling him that he wants to work with him, the notebook which is to the right of the laptop changes positions between shots.
When Sheldon sits down with Leonard to discuss Leonard's experiment, Leonard is actually using the computer that was used by Sheldon in The Fuzzy Boots Corollary (2007) episode.
When Dennis Kim "corrects" Leonard's English for his tendency to end sentences on a preposition, Sheldon chimes in in agreement with Kim. This is a common misconception. There is no rule against ending a sentence on a preposition in English. Dennis Kim and Sheldon are incorrect.