It seems you installed a language pack and not the dictionary. A language pack provides translations for the user interface and appears under "Settings -> Languages", dictionaries for spell checking you install will appear under "Settings -> Dictionaries". This is a misunderstanding we regularly see happen.

You can look here for dictionaries:

• https://addons.mozilla.org/firefox/language-tools/
• https://support.mozilla.org/en-US/kb/how-do-i-use-firefox-spell-checker

Note that for spell check you need a dictionary. The language pack provides string translations for the user interface.

• https://support.mozilla.org/en-US/kb/use-firefox-another-language

on top of https://addons.mozilla.org/firefox/language-tools/ it even tells you what the Dictionaries and Language Packs are used for.

I agree that it looks like you installed a Danish Language Pack and not a Danish Dictionary which is at https://addons.mozilla.org/firefox/addon/dansk-ordbog/ as it would say Dictionaries and not Languages on the left side in the screenshot you posted.

Only a few language locales of Firefox comes with a dictionary due to licensing.

Well that is terribly designed, that's all I can say. Thank you for the help!