The rooftop concert. John's sign-off, "I'd like to thank you on behalf of the group and ourselves and I hope we passed the audition", is a Meaningful Echo of Awesome.
The fact that they nailed the recording of their cover of "Long Tall Sally" in a single take (having performed it so many times before, they were pretty good at it by that point, to say the least).
"Twist and Shout" was also recorded in a single take. What's more, a second take would have not been possible because John's voice was shot. And it was recorded as the last song of the session for their first album. Which (except the four songs from their previous singles) was recorded in a single day. And this while they still were abiding to the normal studio time schedule. While they had a cold.
Until The Beatles broke through in the United States with "I Want to Hold Your Hand" in the winter of 1964, only four other songs by British performers had topped the Billboard pop charts since its inception in 1940. Those songs were the ballad "Auf Wiederseh'n Sweetheart" by Vera Lynn (nine weeks in 1952), the gospel/Sunday school favorite "He's Got the Whole World in His Hands" by Laurie London in 1958, the instrumental "Stranger on the Shore" by Acker Bilk in 1962 and the synth-heavy instrumental "Telstar" by the Tornadoes in early 1963. British popular music had its occasional appeal in the United States through the early 1960s, but the Beatles made British pop music the most dominant style, and began a run of dominance that has yet to be equaled. In 1964 alone, nine songs by British artists reached No. 1 (out of that year's 24 songs that topped the Billboard Hot 100), and by the end of the 1960s, 39 songs from the UK had gone No. 1 on the Billboard Hot 100, with nearly half (18) by the Fab Four (with The Rolling Stones the next closest at five).
For the first week in April of 1964, the band held the top five spots on the Billboard charts (with "Can't Buy Me Love", "Twist and Shout", "She Loves You", "I Want to Hold Your Hand", and "Please Please Me" in that order). This will probably never happen again.
Their first performance on The Ed Sullivan Show drew over 73 million viewers. Still one of the highest rated segments in the history of television.
To make that possible, The Beatles' manager, Brian Epstein, made one of the canniest promotional deals in music history. When he was told by Sullivan's negotiator that the band would only get one appearance as a novelty act, Epstein counter-offered the band would would accept a third of the standard appearance fee of one show for three appearances as the headliner and he himself would cover the travel expenses of the band personally. That proposal was too good for Ed Sullivan to pass up, and The Beatles got the most spectacular American promotion possible that set them up as the music mega-legends they would become.