Just a quick thanks to Carsten Dominik, the author of org-mode, for his amazing support. I upgraded to one of the latest versions of org-mode last night (4.07), and within seconds my CPU was banging on the ceiling, and emacs was unresponsive, requiring me to kill it off.
Carsten was on the case first thing this morning, with around half a dozen emails throughout the day, and a solution early this evening. Sterling stuff.
The problem was that my org-mode file had some (well, quite a lot in fact) multibyte characters, which I am pretty sure got in there from stuff I copied across from a web page into my org-mode buffer. Deleting all these characters was one solution (my first long-winded version), but Carsten also suggested setting the following in my .emacs file, which also fixed it:
(setq org-radio-targets nil)
And the really cool thing is that I can now use 4.07, which has support for mh-e, my favorite mail tool.