There’s so many it’s hard to think of them all.
Let’s start with the fact that Danish is practically two languages in one - the written language and the spoken language. There is very little connection between the two. You cannot look at a word’s spelling and know how it is pronounced, and often it is not pronounced how you would think it is pronounced by looking at the spelling.
The grammar is simple, but it’s so full of irregularities that you basically need to memorise a wide array of words and phrases.
The spoken language has more vowel sounds than the alphabet has vowels, even when Danish has added three extra (æ, ø and å). Each vowel can therefore be pronounced in different ways depending on the word. No, there is no system to tell you which sound is the correct one, you just have to know and memorize it.
Add to this the fact that the pronounciation is quite complicated and basically impossible for foreigners to learn without having a heavy or at least moderate accent.
The spoken language has more vowel sounds than the alphabet has vowels, even when Danish has added three extra (æ, ø and å).
That’s one thing I think English at least did right. Other languages added extra letters and/or diacritics to try to capture all the variations on vowel sounds. But, in most languages there are far more vowel sounds than there are vowels. So, don’t make things unnecessarily complicated by adding extra letters. The one language that seems to do it basically right is Spanish, where there are only about 5 vowel sounds and they use the accent character not to show that a letter is pronounced differently, but just to cue you in on which syllable is accented when it might not be the one you expect. (With a few minor annoying variations, like el and él).