I forgot to include Icelandic and Faroese into the discussion. Icelandic is the most difficult scandinavian language to understand, given you're not an icelander. And icelanders understand other scandinavian languages less than other scandinavians do. (This is party due to the fact that Icelandic is very different from other scandinavian languages and that icelanders are extremely nationalistic, at least concerning the language. They used to be good at Danish until the WW2, but since the independence from Denmark in 1944, they have stopped learning Danish and thus have become linguistically isolated regarding using scandinavian to communicate with other scandinavians.)

The Faroese language in its written form is to some degree comprehensible for all other scandinavian speaking people since it resembles Icelandic in some respects and Norwegian and Danish in some other. Spoken Faroese is, due to some novations, incomprehenseible to all other scandinavian speaking people. Instead, faroese people are really good at understanding spoken and written Norwegian, Danish and Swedish. (Especially Danish since it is the second language in the Faroese islands.) Faroese people may read some Icelandic, but spoken icelandic is completely incomprehensible. (I think that the faroese people would have the greatest possibility to understand northern swedish dialects though since they are used to learn to understand various scandinavian tongues. Northern swedish dialects are almost as archaic as faroese, Dalecarlian is even somewhat more archaic than Faroese though.)