I'm not a native English speaker but I always thought that amount goes with mass nouns (amount of sugar) and number with countable nouns (number of calls). 'A number of people' sounds much better to me.
Am I wrong about English? Is there some shift in meaning between English and Danish? (The help offers 'amount' and 'amount of' as translations for 'mængde'.)
The definition from the Oxford Dictionary is given as "A quantity of something, especially the total of a thing or things in number, size, value, or extent" which to me suggests it can be used for both countable and uncountable nouns. I hear "amount" used this way all the time, but maybe this could be a difference between American and British English
However, you're definitely not wrong to say "A number of people" and it should now be accepted
I concur with the others here who maintain that you should not use "amount", regardless of what you may have heard in America. It seems that the Oxford Dictionary excuses you, but I don't think it does really. As you quote it, it says "something". The Oxford Dictionary does not refer to people as belonging to the category of "something", I hope. I would also never use "amount" for inanimate countable nouns, although your reference apparently shows that one may. Especially, referring to animate countable nouns, one should not use "amount". Use "number" or, even better, when dealing with people, "a crowd".
Mångde has several meanings. One is "amount" and a second meaning is a "crowd" for a large number or group of people at an event. As a native American I would never say an amount of people but a crowd of people or a group of people or even number of people are all acceptable uses in American English. Given the meanings for "mængde" a crowd of people seems the best translation and Duolingo accepts that as correct.