Michelle Shocked’s Anchorage poignantly references one of Michelle Shocked’s own songs, that has been forgotten by an old friend of hers:
Billy Joel’s song The Entertainer is a cynical reflection on his sudden fame and fortune after his first big hit, Piano Man.
I am The Entertainer, I’ve come to do my show
You’ve heard my latest record, it’s been on the radio
It took me years to write it, they were the best years of my life
It was a beautiful song, but it ran too long
If you’re gonna have a hit, you gotta make it fit
So they cut it down to 3:05
(Piano Man being quite a long song on the LP, nearly 6 minutes long, but the “single” version of it released for Top 40 radio was edited down to 3:05.)
Song Sung Blue, Neil Diamond:
*
Me and you are subject to
The blues now and then
But when you take the blues
And make a song
You sing 'em out again*
Perhaps along the same lines, some of the tracks on the Kinks’ Lola vs. Powerman and the Moneygoround album are about the music biz, including “Moneygoround”
and “Top of the Pops”
No mention of what the record in question is, although I’ve seen the album described as a concept album about making a hit single, with “Lola” being the hit single.
What about Peter, Paul, and Mary’s “I Dig Rock and Roll Music”?
“Miss Williams’ Guitar” by The Jayhawks is very similar in nature to Killing Me Softly, in that it is a song about the experience of watching another performer. Specifically, it is about Victoria Williams, then the girlfriend and later the wife of songwriter Mark Olson:
Miss William’s guitar
Miss William’s guitar
I remember watching her play
And the whole damn crowd
Seemed so far away
Feed the Fire, by Happy Rhodes quotes Running Up That Hill, by Kate Bush.
I’m channeling Equipoise today. 
“Standin’ on a corner in Winslow Arizona
and I’m quite sure I’m in the wrong song”
-Tori Amos “In the Springtime of his Voodoo”
The title (at least as it appears on my GH Live in Japan CD) is “Got My Mind Set on You”; no “I,” no parentheses.
I was going to post this one. Lennon’s How do you sleep? has a similar theme.
Ah, wasn’t sure of that. But regardless of the title, as sung, the repetitive phrases in the respective songs are each seven words long. 
I heard Weird Al does an unreleased song at his concerts titled “It’s Still Billy Joel to Me” TTTO “It’s Still Rock And Roll To Me” but I don’t know if the lyrics comment directly upon that particular song, or are they about Billy Joel’s songs in general.
*** Ponder
Jeez, Weird Al’s ‘Smells Like Nirvana’ is specifically about ‘Smells Like Teen Spirit’ and how no one can understand the words. He even got Cobain’s blessing for it.
And the video even uses the same set and most of the same extras. Can’t get more on it than that.
Technically this one is about a record rather than the song per se, but I think it’s worth mentioning: I Can’t Get “Bouncing Babies” by the Teardrop Explodes by the Freshies.
The Johnny Cash song Daddy Sang Bass is essentially a song about the singer’s family singing “Will the Circle Be Unbroken?”.
I did a thread not too long back about songs with sequels that is somewhat relevant.
Life is a Rock by Reunion names and references tons of songs and musicians.
Billy Joel’s We Didn’t Start the Fire does the same, but with less focus on music.
The Beatle’s Back in the USSR is an ironic tribute to Back in the USA.
Charlie Daniel’s The South’s Gonna do it Again is about southern music and musicians.
Chuck Berry’s Roll Over Beethoven.
Chuck also did a song called Bio where he sings about his own musical roots.
Calling Elvis by Dire Straits.
Jackie Wilson Said by Van Morrison
Land of 1000 Dances by Wilson Pickett
I Sang Dixie - Dwight Yoakam
In the country vein, George Jones’ Who’s Gonna Fill their Shoes? mentions several titles in tribute to their respective artists.
http://www.lyricsdownload.com/george-jones-who-s-gonna-fill-their-shoes-lyrics.html
It Wasn’t God Who Made Honky Tonk Angels by Kitty Wells was written in response to (and to the tune of) The Wild Side of Life by Hank Thompson.
It wasn’t God who made honky tonk angels
as you said in the words of your song
Too many times married men think they’re still single
That has caused many a good girl to go wrong
Parts of Whiskey Bent and Hell Bound by Hank Williams, Jr. are about how his father’s songs affect him:
*Play me some songs about a Ramblin’ Man
Put a cold one in my hand
Cause you know I love to hear those guitar sounds
Don’t you play I’m So Lonesome I Could Cry
Cause I’ll get all balled up inside
And I’ll get whiskey bent and hell bound
…Yeah, old Hank’s songs
Always make me feel low down*
How about El Paso and El Paso City by Marty Robbins? In El Paso, Robbins tells the tale of how he feels he was the cowboy in the song El Paso.
SSG Schwartz