Danish radio had an interview with a linguist who has studied the language of Swedes working in Danish shops (if you visit the Field’s shopping mall there is a pretty big chance that you’ll be served by a Swede).
Given that spoken Danish and Swedish are fairly different, the subject is pretty interesting – speaking from personal experience the other way around, I would say that getting the words right is fairly easy. The Swedish “r” is tricky and Swedish also has an sh/ch-sound which is difficult for Danes and getting the tone and melodic accents right is almost impossible.
Oh, and in case any old students wonder – yes, I did write my emails in Danish on purpose.
The entire programme (in annoying Microsoft Audio format) is here.