I'm very pleased to say that the Typepad engineers have fixed the issue I've been having with some of the categories.
Even better they managed to connect the broken links (or whatever had happened) so the Green Card and Visa Category points back at all 64 of the posts I'd designated as falling under that heading. I was really not looking forward to trawling the archives to re-categorise those posts, and now I don't have to! Hooray!
Even better Typepad are giving me a free month of blogging to compensate for the issues I've been having, which I really wasn't expecting them to do.
All in all I feel particularly warm and fuzzy towards the Typepad help-desk, and their good friends the IT genii today. They rock.