> \setuphead[subsection][style=cap]  %aborts compilation. (But
> "slanted" works)
>
> I also unsuccessfully tried "style=\cap" (or \kap etc.), "command=
> \cap" etc.  (But style=\sc works. I don't want small caps, though).



Did you try \WORD{} ?
see http://wiki.contextgarden.net/Basic_Text_Formatting

AFAIK \cap and \kap are LaTeX...

Greetlings, Hraban