Which thyroid disease do you have?
The prescribing information given for Ziac says that if you have hyperthyroidism, you may not be able to take the drug. If you do, you will need more vigilant monitoring than someone without hyperT needs. Apparently, by making the heart beat more slowly, it masks the effects of high thyroid hormone levels. By inference, it would seem it could also mask the effect of too high a dose of medicine used for hypOthyroidism as well.
I have read articles by cardiologists who say beta blockers in general should be avoided by hypoT patients as well, since their hearts already tend to beat too slowly, and the beta blocker will exacerbate the effect.