Sort of going to an earlier post about board selection
But if the board picture in the lower left could be a little more "interactive" and allow any other boards to be selected.
Could be more useful if moving a thing to a different board.
Maybe smaller pics of boards available to the cloud... Point and shoot 
EDIT:
Just found the other way to do this but a secondary method might be worth putting in ?
Thanks for the advice! Changing the board associated to a thing is a feature we do not support yet, but we are collecting feeback about it and it's probable that it will be available by the end of the year.
Just another wild thought and sort of linked to sharing a thing.
If SHARE THING ever becomes a feature (high on wish list LOL) then where it says "ASSOCIATED BOARD" on the lower left a link back to products like you have done in another area. (sales leads)
ANOTHER EDIT LOL :
Having the available boards at the lower left would also allow quick change between things.
Not sure how easy to implement ? (Wait i said that already OMG)