I have found out some more infomration. This problem is at least partly to do with NextGEN, but not completely.
With NextGEN activated:
With Post Formatting selected (Add toolbar & buttons to textareas…) neither the border nor the html buttons show up.
With Post Formatting not selected, the border is present (i.e. it works)
With NextGEN deactivated:
With Post Formatting selected the buttons appear but still no border
With Post Formatting not selected, the border is present again.
Deactivating all other products makes no difference.
