Ubbi Dubbi, spoken by Penny and Amy in this episode, was popularized by the 1970's children's show Zoom (1972). In this secret language, the letters "ub" are added in front of each vowel sound in every syllable of an existing word, e.g. "hello" becomes "huballubo". It may also have been the inspiration for Amy's invented language 'Op' from The Skank Reflex Analysis (2011), where the letters "op" are added to each consonant in a word (so "hallo" would become "hop-a-lop-lop-o").
Sheldon asks Amy to sing 2001: A Space Odyssey (1968). The proper name is 'Also sprach Zarathustra', AKA Opus 30 by Richard Strauss.
Apparently, aside from "Soft Kitty" (as seen in The Anxiety Optimization (2015)), 'Also Sprach Zarathustra', the main theme from 2001: A Space Odyssey (1968) can also put Sheldon to sleep.
This episode was the last one broadcast prior to the 2016 Presidential Elections between Hillary Clinton and Donald Trump, which were won by the latter. All of Chuck Lorre's Vanity Cards starting with this episode and ending with The Romance Recalibration (2017) comment on the election and the result.
During the Fun With Flags segment, Sheldon has chosen to display the flag of the apartment he shares with Leonard, even though the show is being streamed from Penny's apartment. Given Sheldon's peculiar affinity for rules and regulations, it's an oddity that he would make this choice.