After Penny fails to convince Sheldon that Dr. Nowitzki is romantically interested in him, she looks over to the painting Amy commissioned of the two of them and apologizes to it. However, the painting was relocated to Leonard and Penny's apartment earlier in the season, so it wouldn't have been in Sheldon and Amy's apartment for Penny to see.
In the pre-titles scene Sheldon once again says that splitting an infinitive and ending a sentence with a preposition are wrong. While it suits the character's well established pedantry, it is also well established that Sheldon actually knows about most of the things he complains about. As a know-all, he would be well aware that both those "rules" are actually considered to be "superstitions" by grammarians who dismiss them (and many other similar rules taught by high school English teachers) as utter nonsense.
The photo of Princeton University is of Nassau Hall, the oldest building on campus and not where Amy rented an apartment.