After Sheldon declares he had "unfriended" Leonard, the list of his Facebook friends is displayed and Leonard is still there.
Sheldon's Facebook page is shown, and his friend list includes: Amy Farah Fowler, Anthony Robinson, Gary Torvinen, Henry Johnson, Jason W., Jess Ambrosetti (the coordinating producer of the show), Justin Hetzel, Kirsten G., Leonard Hofstedter, and his mom, Mary Cooper. After this page is displayed he claims to unfriend Howard Wolowitz but Howard wasn't listed as a friend. The names are shown in alphabetical order by first name, so Howard was already unfriended before the page was displayed.
When Sheldon knocks the first time on Penny's door, she immediately shouts "Who do we love?" anticipating that he will say "Penny". However, after the first knock and before he says her name, she has no way of knowing that Sheldon is there or that her name will be called. Nobody else knocks on Penny's door in the particular pattern used by Sheldon. She may have been saving that response for the next time he uses it.
After presenting Amy with the Relationship Agreement, Sheldon gives her time to read it while he sets up his notary stamp. Notarization by a party to a contract would be ineffectual, so there would be no point in his doing so.
Sheldon presents his idea to Amy of him NOT objecting to them NO longer characterizing her as NOT his girlfriend. Amy tells him to try again without using a quadruple negative when he actually used a triple negative.
The fourth negative is the word object, meaning he would not be against no longer characterizing Amy as not his girlfriend.
Sheldon states people cannot be owned as property since 1863 when Abe Lincoln freed the slaves, however the slaves in border states were not freed until the thirteenth amendment was ratified in 1865 and, did not take into effect until after Lincoln was killed.
Even though Amy says comics are "lame-o", she has a super-hero mosaic on the wall of her apartment. It can be seen while they discuss the Relationship Agreement.