Nicola:

There's been quite a bit on the net re: relationship between celiac and
thyroid as well as other diseases. The key guy tracking info on the net
is Don Wiss. Check out his "gluten-free page" on celiac disease,
http://www.panix.com/~donwiss/

As for supplements, I've had luck with calcium and Vitamin D (for
aches/pains), essential fatty acids like evening primrose oil/borage
oil, staying away from separate kelp supplements (but a little bit is in
my herbal multi) and some special herbal blends my herbalist recommended
for liver support.

The Zone diet is very good for Thyroid patients.  There are a number of
us who had some luck losing a bit on it. I too lost nada on weight
watchers, but a bit on zone. Best part of zone is it stabilizes blood
sugar, and I had tons more energy, far less "hypo crashes" and general
better well-being!

Take care!

Mary