Change your langauge and common name place setting to Danish and Denmark, respectively.
Scroll through your observations or look at observations made in Denmark. Some observations will show the English name rather than the scientific name if there's no Danish name, or will sometimes show the Englihs name even if there is a Danish common name.
"My observations" screen: We display the "species guess" field, saved locally in DB. When you switch languages, we don't immediately update the species guess for all observations (this requires basically calling iNat APIs for all observations to retrieve latest species guess in the new language. So this won't happen immediately, and will happen in the background.
"Explore" screen: I couldn't recreate this (displayed the proper names) - can you give some specific examples? (which taxon wasn't being displayed properly in explore screen)
Version 1.27.4 (546)