Now as for Swedish, what trips me up is that I've met so many Swedes that (otherwise) speak great English, but seem to pronounce J sounds in a distinctly Swedish way when speaking English. I've had fluent English-speaking Swedes in a university setting asking if I want to hear a "yoke" (joke) and or maybe telling me about their "yeans" (jeans). It's so weird. It's a bit like how many French people seem unable to pronounce an H when speaking English, but Swedes are damn good at English, unlike the average French person.
Likewise, I can identify English with a Danish accent pretty quickly, but I can't for the love of me speak it, because I'm not good enough at Danish. But a dead giveaway is that Danish realizes 'R' as [ʁ], and many Danes pronounce it the same way when speaking English. :-P And there's something with the vowels that's just weird that Danish people do... I can't put my finger on it.
(I have the opposite problem, I can't make that 'R' sound at all, which is why my Danish sounds pretty funny to native Danes.)