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A line from the lyrics appeared in the 'scrapbook' section of radiohead.com:
words are blunt instruments
The official 2006 Radiohead calendar contained a page which featured related lines (click to enlarge):
On September 28th 2006, the following messages were posted on Dead Air Space. They both mention 'Pay Day', and it's very likely that 'Pay Day' is the working title of 'Open Pick':

DAS
DAS
'Open Pick' 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:
A few lines from the lyrics were posted on Dead Air Space during the period when the band was working with Mark "Spike" Stent:

DAS
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. 'Open Pick' was one of these, and would indeed be played (click image for full size):
On may 6th 2006, the song was premiered live in Copenhagen. This video was edited for this website from multiple video sources:
In May and June 2006, 'Open Pick' was played live eight times. In contrast to the first half of the song, the lyrics after the instrumental break varied slightly with each performance. To be precise, only two of the verses were different each time. The "stable" sections of the lyrics aren't included in the following overview:


Copenhagen 1:

before you run away from me
before you're lost between the notes
the beat goes round and round
the beat goes round and round

[...]

before the night owl
before you start unravelling
just as you take a mic
just as you dance, dance, dance, dance...
Amsterdam 1:

before you take my hand
before you start unravelling
the beat goes round and round
the beat goes round and round

[...]

before you start unravelling
before you take your last peek
before you take a mic
before you dance, dance, dance, dance...
Wolverhampton 2:

before you run away from me
before you're lost between the notes
the beat goes round and round
the beat goes round and round

[...]

before you run away from me
before you start unravelling
before you take a mic
just as you dance, dance, dance, dance...
London 2:

before you run away from me
before you're lost between the notes
the beat goes round and round
the beat goes round and round

[...]

before you run away from me
before you put a spell on me
just as you take a mic
just as you dance, dance, dance, dance...
Philadelphia 1:

???
just as you ???
and the beat goes round and round
the beat goes round and round

[...]

before you ??? away from me
before you go and spill the beans
before you take a mic
just as you dance, dance, dance, dance...
Toronto 1:

before you run away from me
before you're lost between the notes
the beat goes round and round
the beat goes round and round

[...]

before you run away from me
before you start unravelling
before you take a mic
before you dance, dance, dance, dance...
Montreal 2:

before you run away from me
before you're lost between the notes
the beat goes round and round
the beat goes round and round

[...]

before you run away from me
before you're lost between the notes
before you wake again
before you dance, dance, dance, dance...
Chicago 1:

before you run away from me
before you're lost between the notes
the beat goes round and round
the beat goes round and round

[...]

before you run away from me
before you're lost between the notes
just as you take a mic
just as you dance, dance, dance, dance...
The fact that the song was played only rarely (compared to other new material) may have had something to do with the band being insecure about it during this period. From a post on the message board of ateaseweb.com:

atease
On June 15th 2007, Nigel posted a video on Dead Air Space, that showed the playback of a reel of assembled tape snippets, which were cut out during the editing process.
At the beginning the reel contains 5 fragments from the finished recording of 'Open Pick'. Below you find these fragments, some of which actually flow seemlessly into each other and can be combined if one switches the order around and reverses the bits that were backwards on Nigel's reel:

Click here for a more detailed description of this reel, including all 20 snippets in isolation.
For the webcast on november 9th 2007, Adam Buxton and Garth Jennings made a video for this song where the band, wearing helmet cameras, mimed along to the album version:
In mid december 2007, a different arrangement of the song, performed only by Thom, Jonny and Ed, was part of the Scotch mist film produced:
On January 15th 2008, Thom mentioned the release of 'Jigsaw Falling Into Place' as the first single from In Rainbows in this entry on Dead Air Space:

DAS
'Jigsaw Falling Into Place' was released as the first single from In Rainbows on january 14th 2008. It entered the UK Singles Charts at #30 and had left the Top 40 the following week.

The 7" vinyl single was backed by Thom's november 2005 From the Basement solo piano performance of 'Videotape', while the CD single featured Thom's solo piano versions of 'Down Is the New Up' and 'Last Flowers' from the same session as b-sides.
'Jigsaw Falling Into Place' was not performed during the touring for The King of Limbs.