Throughout all of the verses of "Secret", the dominant is always a dominant seventh - in this case B7. In the middle 8 ("I've known a secret for a week or two/Nobody knows, just we two"), however, we hear minor dominants (B minor) on both iterations of the word "two". Listen to these two MIDI examples, the first of which using the minor dominant (as is heard in the final product), the second of which uses the more common major dominant. The difference is subtle but significant.
As a side note, the opening lines of the first verse ("Do you want to know a secret? Do you promise not to tell?") are taken nearly word for word from the song "I'm Wishing" from the 1937 Disney film Snow White and the Seven Dwarfs. Julia, John's mother, used to sing him the Disney tune as a lullaby. Though "I'm Wishing" bears no musical resemblance, the lyrics made their way into Lennon's rock song.