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The lyrics of 'Videotape' were possibly inspired by the 1998 Japanese film Wandâfuru Raifu (English title "After Life") . In the film, newly deceased people describe their happiest memory to a film crew, who recreate it, film it, and commit it to videotape. The deceased take the videotape with them into heaven.
During the Kid A era, this page appeared on under the title 'too late':

every bad act
is stored on a magnetic tape
which we retain. kept in a secret vault
and evaluated
repeated and repeated with your code name
at the top of the file.
to be reviewed at your departure
for the pearly gates.
The official 2006 Radiohead calendar contained a page which featured related lines (click to enlarge):
How would you describe the status of the next Radiohead album?

Thom: We have roughs of things. We have Maybe half of something so far. There's another six tunes we haven't started playing live yet. There's one called "Videotape" that's really cool. It's got lots of cyclical melodies. It's one of the first things we had. We were smashing our heads against the wall, trying to figure out what to do with it. Sometimes that drives me crazy.
'Videotape' was one of the titles that appeared on the blackboard the band used during two weeks of rehearsals from september 19th to 30th 2005. At the end of that session, Colin posted a picture of this board on Dead Air Space on september 30th, unfortunately (and probably intentionally) in rather low resolution, so that some of it can't be deciphered:
On February 24th 2006, these pictures were posted on Dead Air Space, showing the band working on this song:

On March 8th 2006, shortly after sessions with Mark Stent had come to an unfruitful end, another photo of a blackboard (and a perhaps slightly worried Ed) was posted on Dead Air Space. A tour had been scheduled for may and june to escape the frustration of the recent sessions and to breathe new life into the project. Rehearsals for the upcoming dates had begun recently, and this board shows which new songs were at this point considered for inclusion in the setlists. 'Videotape' was one of these, and would indeed be played (click image for full size):
On April 5th 2006, Thom posted a good part of the lyrics on Dead Air Space:
This photo was also posted on Dead Air Space. The initial name of the image file was 'Videotape!Again!.jpg', this was later changed to 'rehearsalweek':
In November 2006, Thom performed the song for the first episode of Nigel Godrich's From The Basement programme. At this point it still includes the lines "I'm talking to you/after it's too late/from my videotape", which were seen in one of the pages of the 2006 calendar and would later be omitted from the song. This performance of 'Videotape' was released as a b-side on the Jigsaw Falling Into Place single on January 14th 2008.

when I'm at the pearly gates
this'll be on my videotape
my videotape

when Mephistopholis is just beneath
and he's reaching up to grab me

this is one for the good days
and I have it all here
in red blue green
in red blue green

you are my centre when I spin away
out of control on videotape
on videotape
on videotape

this is my way of saying goodbye
because I can't do it face to face
I'm talking to you
after it's too late
from my videotape

no matter what happens now
I won't be afraid
because I know
today has been the most
perfect day
I've ever seen

On June 18th 2006, the full band premiered the song at the show at London's Hammersmith Apollo. 'Videotape' opened the set:
In early November 2007, a video for this song was prepared by Thom and Nigel for Radiohead's "thumbs_down" webcast.

On February 12th 2008, Thom also posted the video on Dead Air Space:
Live performance #91 during the making of The King of Limbs:
91. february 25th 2010 Corn Exchange Cambridge UK Link
As part of the initial touring for the "Atoms For Peace" project, the song was played on two occasions during Thom's solo acoustic section:
  Thom solo section [prev. released songs] oct. 2009 april/august 2010
Videotape [2] 17 01
I Might Be Wrong [1] 01
Like Spinning Plates [3] 08 11 14
Fog [1] 06
Everything In Its Right Place [6] 05 06 10 14 17 18
Airbag [3] 11 15 18