These were quickly compiled off the top of my head, so feel free to holler at me for omitting Her Majesty 
Error.
Other-Why Don’t We Do It In The Road.
A lot of those songs, it’s news to me that they are underrated. There are siome classics on that list.
I would go for:
I’ll Be Back - Seems to generally be regarded as minor album filler, but I absolutely love it, it’s a fantastic tune.
Baby You’re a Rich Man - some people actually rate this as one of the Beatles’ stinkers, which amazes me. (Haven’t they heard the white album? ;))
You’ve Got My Name (Look Up the Number) - ditto, pretty much
“Hey Bulldog” has one of my favorite bass lines ever.
One of my very favourite Beatles songs is Here Comes the Sun by George Harrison on Abbey Road. I don’t know if it can fit in the underrated category, but I don’t hear it mentioned as much as their hit songs.
Happiness is a warm gun - Brilliant John song that many consider a joke, but it is so Edgy!
You’re Gonna Lose that girl - Another great Lennon song. It’s also a funny concept–taking a girl out and treating her fine, just to spite the other guy for treating her badly.
Flying - Mostly Instrumental song from Magical Mystery Tour - one of the most beautiful 2-minute or so pieces of music ever made
I’ve Got a Feeling - It’s on the list, and the parts where John and Paul are singing they’re separate “songs” intermittently are about as brilliant as they got.
F
Apart from the ones I picked, I’d like to add “Things We Said Today.” Oh, and “No Reply.”
And I’ll agree with Ximenean on “I’ll Be Back.”
Moving from IMHO to Cafe Society.
I voted for several, but my number 1 choice is Rain. I like Paperback Writer, but I think it unfairly overshadows its B-side. I hear and see references to PBW everywhere, but I can’t remember the last time I heard Rain when I wasn’t specifically listening to it.
Tomorrow never knows - This was always oneof my favourites , and in my mind it was 20 years ahead of its time
In addition to some of the others that have been mentioned, I’d like to nominate Geroge’s “Savoy Truffle.”
From this list, I went with “Cry Baby Cry.” But for the most truly underrated, I’d vote for another White Album track: “Long Long Long.” One of the most hauntingly beautiful things in the Beatles canon, but a lot of people seem to hate it. I can’t understand that.
Anyway, the most underrated Beatles cut has to be a Harrisong.
You know what? I take it all back. The most underrated is still on the White Album, but it’s “Revolution 9.” People really don’t get that one.
Your list doesn’t have my favorite Beatles song that hardly anyone else likes: Within You Without You. I don’t care what anybody says, the song is beautiful and the rhythms and instrumentals are brilliant.
Um, om, …and shit.
Lot’s of Revolver on that list…
On that note, I’d have to throw my vote behind Paperback Writer. I’ve always heard it described as “some fluff The Beatles did before they became THE BEATLES.” But I think it’s a fantastic song and infinitely sing-along-able.
I’m going to nominate “If I Needed Someone”.
Just off the top of my head, you missed:
[ul]
[li]“Long Long Long”[/li][li]“Mother Nature’s Son”[/li][li]“She Came in Through the Bathroom Window”[/li][li]“Dig a Pony”[/li][li]“The Continuing Story of Bungalow Bill”[/li][li]“Rocky Raccoon”[/li][li]“Do You Want to Know a Secret?”[/li][/ul]
ETA: And I voted for a crap ton of your choices. Including your namesake.
“Julia” is one of my faves that is never on the radio. Beautiful little song.
I voted for Cry Baby Cry, Run for your Life, and Dear Prudence. I’ll add Within You-Without You, Tax Man, Fool on the Hill and Julia (the “her hair of floating sky is shimmering, glimmering” always gets me for some reason).