Interesting tread and even if most posts are of older date I will contribute as I havnt seen many Danes comment.
I’m Danish living south of Copenhagen and I can understand both Norwegian and Swedish fairly easy and I think that if i moved to either country I would get the language quite fast they are so similar. In my previous job I regularly communicated with our office in Oslo and Stockholm and we almost always spoke our own language. Personally I have a tendency to mix Swedish and Norwegian because I know that there is a difference in the languages but I don’t really know the correct word. So it is actually easier for the other to understand if I just stick to Danish 100%.
One of the things people have talked about is that when speaking Norwegian and Swedish are much more closely related and the Danes are speaking with a potato in the mouth. I can confirm that we do not have a potato in our mouth when we speak, but from my point of view I would say Danish is perhaps more influenced by German (our way of counting are similar to german) and we have a tendency to pronounce one word stop a bit and then pronounce the next word stop etc. But the Swedish and Norwegian language is a kind of a song where the words flow together in one long sentence.
In writing Norwegian is very easy to understand especially bokmål it is kind of Danish for people that don’t spell so good. Danish has a lot of differences in the written language and the spoken and if you write like you hear it you are often wrong. One example I remember from one of my first tripås to Norway as a kid was chocolate, in Danish it is spelled “chokolade” almost the English way but its pronounced like the Norwegians spell it “sjokolade” also many of the words are the same in Danish and Norwegian. Swedish is a bit harder as there is more differences, but I guess most Danish people could read a book in Swedish, it might take a bit longer but its totally doable.
There was also a guy that asked about learning one language and understanding the others. My wife is not a native Danish speaker as she immigrated from Asia to Denmark at the age of 14. She speaks Danish fluently and I would say her accent is about 98% Danish (some people thinks she is adopted from her accent). She has a very hard time understanding both Swedish and Norwegian. But I’m sure that if she moved there she would learn it quite fast as she is already fluent in Danish.
And as a last note, nobody understands the Swedish chef it was newer a real language just sounds that sounds like Swedish.