Do lots of people get thyroiditis, or is it unusual?

Depends on type. Chronic thyroiditis (aka hashimoto's) is very common. It causes underactivity of the thyroid. Acute thyroiditis is much less common. There is often pain and it causes a temporary rise in thyroid hormone levels.
Not common. Inflammatory thyroid condition of thyroiditis is not too common. It seems to occur more in women (hashimoto;s thyroiditis). It can resolve on its own for many. I am not aware of a known reason why this occurs.