Hans and list,

Previous to the 20140316 beta, we were able to prevent text backgrounds 
from bleeding over the footnote space with

    \chardef\kindofpagetextareas\plusone

as you described in a 2008 list entry. While the problem it resolves is 
still there, the fix is now broken. The background on the following page 
is starts too far down the page (although it appears to have the proper 
depth).

The following example demonstrates the problem. Sorry for its length.

    \setuppapersize[A6][A6]

    \definetextbackground[blockquotebackground]
                 [
                   location=paragraph,
                   background=color,
                   backgroundcolor=gray,
                   backgroundoffset=.25em,
                   frame=off,
                 ]

    \definedelimitedtext[BlockQuote]
    \setupdelimitedtext
       [BlockQuote]
       [
         leftmargin=1pc,
         rightmargin=1pc,
         before={%
                  \blank[halfline]%
                  \startblockquotebackground%
                  \setupindenting[next]%
                },
         after={%
                  \stopblockquotebackground%
                  \blank[halfline]%
               },
       ]

    \starttexdefinition startAttribution
       \setupnarrower[left=1pc]
       \startnarrower[left]
         \leavevmode\llap{{--\,}}%
    \stoptexdefinition

    \starttexdefinition stopAttribution
       \stopnarrower
    \stoptexdefinition

    %% The following prevents the background from overlaying
    %%   footnotes. Found in a 2008 post, still not in the wiki.
    %% http://www.mail-archive.com/ntg-context%40ntg.nl/msg15681.html
    %%
    %% With the 20140316 beta, things have changed again. Now the
    %%   problem without it is still there, but with it the background
    %%   is misplaced on the second page of a two-page background.
    %%
    \chardef\kindofpagetextareas\plusone

    \starttext

    \startBlockQuote
       Honorar und Verbot des Nachdrucks sind im Grunde der Verderb der
       Litteratur.

       Writing for money and reservation of copyright are, at bottom, the
       ruin of literature.

    \startAttribution
       Arthur Schopenhauer, chapter {\sc xxiii} \quotation{Ueber
       Schriftstellerei und Stil} {\em Parerga und Paralipomena} page
       420\footnote{Translation by Thomas Bailey Saunders, {\em The Art of
       Literature: A Series of Essays} page 3}
    \stopAttribution
    \stopBlockQuote

    Again.

    \startBlockQuote
       Honorar und Verbot des Nachdrucks sind im Grunde der Verderb der
       Litteratur.

       Writing for money and reservation of copyright are, at bottom, the
       ruin of literature.

    \startAttribution
       Arthur Schopenhauer, chapter {\sc xxiii} \quotation{Ueber
       Schriftstellerei und Stil} {\em Parerga und Paralipomena} page
       420\footnote{Translation by Thomas Bailey Saunders, {\em The Art of
       Literature: A Series of Essays} page 3}
    \stopAttribution
    \stopBlockQuote

    Again.

    \startBlockQuote
       Honorar und Verbot des Nachdrucks sind im Grunde der Verderb der
       Litteratur.

       Writing for money and reservation of copyright are, at bottom, the
       ruin of literature.

    \startAttribution
       \leavevmode\llap{{--\,}}%
       Arthur Schopenhauer, chapter {\sc xxiii} \quotation{Ueber
       Schriftstellerei und Stil} {\em Parerga und Paralipomena} page
       420\footnote{Translation by Thomas Bailey Saunders, {\em The Art of
       Literature: A Series of Essays} page 3}
    \stopAttribution
    \stopBlockQuote

    \stoptext