UPDATE: True to form, I will share some tips for using Duolingo, getting the most out of it, and doing so efficiently.
1) The smartphone apps (or at least the Windows Phone app) are much less forgiving. The app grants you three lives when you start a topic such as "Basics". (The list of topics goes far beyond the five in the picture below.) If you browse to Duolingo's web site, you essentially have unlimited attempts to complete a topic.
2) Don't bother with punctuation. Unless there's a comma mid-sentence, Duolingo doesn't care about question marks, periods, or exclamation marks in either language. This means you don't have to know where all those keys are, in either keyboard layout. (See my earlier post about keyboards.)
Duolingo does care about capitalization, as appropriate for English or Swedish. You don't have to capitalize the first word of a sentence, though. So don't bother.
3) For Duolingo, always use the Swedish keyboard layout (so you have ö, ä, å handy) and omit contractions in English. When going from Swedish to English, type out (for example) "cannot" instead of "can't". The apostrophe key is in a weird place on the Swedish keyboard. Faster to avoid it.
4) Use the gamification features in Duolingo. Keep your streak going, take the speed tests once in a while, maybe bet some points on completing a 7-day streak. Beware that the mobile app and web app aren't necessarily tallying your progress the same way. For instance, if you do the last day of your 7-day streak on the phone app but you did the first 6 in the web version, you may break your streak. (If you care.)
5) Tinycards -- Duolingo's other website / app -- provides flashcards to help you learn words. The card "stack" for Swedish seems really basic. Maybe it will get better with time.
6) Duolingo sells, delivers, and scores an assessment test for people who are learning English. Pretty cool -- the FAQ is here.